CHICAGO — Perhaps the post-Thanksgiving blahs are over for the Dallas Cowboys, assured of their first winning season in five years after a 41-28 thumping of the Chicago Bears Thursday night.

“We’ve had enough 8-8’s,” said quarterback Tony Romo, who, on a very efficient night, completed 21 of 26 passes for 205 yards and three touchdowns.

Dallas, which always hosts a holiday game, finished at .500 the last three years in large measure because of an 8-11 record after Thanksgiving. But in this, the Cowboys’ first post-Thanksgiving game of 2014, they built a 35-7 lead after three quarters and coasted to improve their record to 9-4, including the NFL’s only perfect road record (6-0).

Chicago fell to 5-8 and saw its already-slim playoff hopes virtually extinguished.

“We’re not doing the things in all three phases that we need to do to win on a consistent basis in this league,” Bears head coach Marc Trestman said. “We couldn’t hold up stopping the run. … When we did have a chance offensively, we didn’t move it consistently. … We’re making too many mistakes, too many penalties in all three phases, certainly tonight, which debilitated us.”

NFL rushing leader DeMarco Murray gained 179 yards on 32 carries and caught nine passes for another 49 yards for the Cowboys, who, from early in the second quarter, scored touchdowns on five consecutive possessions and scored points on seven consecutive possessions.

“He did a good job being persistent,” said Jason Garrett, the Dallas coach. “Like a lot of great backs, he gets better the more he touches the ball.”

The Cowboys started slowly. In a scoreless first quarter, their first two drives ended on a third-down sack and a third-down overthrow by Romo when tight end Jason Witten was wide open down the middle.

But that was the extent of Dallas’ misplays while the game still was competitive — and also the end of the Cowboys’ third-down misfires; at one point, they converted six consecutive third downs into first downs.

Leading 14-7 at the half, Dallas began to put the game out of reach with its next score, set up when defensive end Anthony Spencer knocked the ball out of Matt Forte’s grasp after a Chicago screen pass near midfield. Cornerback Sterling Moore picked up the loose ball and returned it 16 yards to the Chicago 31-yard line.

On third down from the 24, Romo scrambled away from pressure toward the right sideline and threw a perfect pass to Cole Beasley, who got behind safety Chris Conte, for his second touchdown of the game and a 21-7 lead.

Chicago’s ensuing possession was a 3-and-out and, even after a Dwayne Harris punt return for an apparent touchdown was nullified by penalty, the Cowboys struck quickly. Romo threw to Dez Bryant for 43 yards on the first play and then, on third down, Romo threw a 6-yard touchdown pass to backup tight end Gavin Escobar.

Before the third quarter ended, Dallas scored again on a 17-yard run by Joseph Randle to make the score 35-7 — and the game was never in doubt even though Chicago scored three touchdowns in the first nine minutes of the fourth quarter. The comeback attempt, too little and too late, ended with an end-zone interception by Orlando Scandrick with 1:29 remaining.

Jay Cutler, the Bears quarterback, had a statistically effective night — 32 of 46 for 341 yards and two touchdowns — but more than half his yardage came in fourth-quarter garbage time after the game essentially was over.

Cutler’s playoff history is not unlike Romo’s; he has reached the postseason game only once in eight previous seasons and apparently won’t this year, either, although the Bears thought they were ready to make a run for it with an offense that was re-tooled a year ago to become one of the best in the league.

Given expectations, Cutler was asked where this season would rank among career disappointments.

“Probably number one,” he said.”

Perhaps mindful of their recent December history, it was apparent early on that the Cowboys were going to play aggressively. Early in the second quarter, Garrett ordered the offense to remain on the field on two consecutive fourth-and-one situations, and Murray converted both of them with runs, the second producing the game’s first touchdown.

Dallas had gone for it on fourth down only four times in the season’s first 12 games.

“You want to be aggressive, and that’s the style of football we want to play,” Garrett said.

What the Cowboys said:

“It feels good to win, but we have to keep on moving and keep on attacking. This (season) is an opportunity, and we have to take advantage of it.” — Wide receiver Dez Bryant.

“When you’ve got a guy like (DeMarco Murray) that can run the ball like that and do it for a whole game, it changes the complexion of the game. It keeps their offense off the field and grinds the clock. When you can run the ball like that, you’re going to be a good team offensively, always.” — Wide receiver Cole Beasley.

What the Bears said:

“We’ve got to play like we did the middle of the third quarter on. We’ve got to play up-tempo, we’ve got to have some energy out there. We’ve got to have guys making plays. Obviously, we want to run the ball better. … We’ve got to do all those things. We’ve got to quit with the penalties. Guys in that locker room, especially offensively, we know we haven’t lived up to expectations and we’ve got a chance these last three games just to play better. We’re obviously not going to fix the season by any means, but trying to end it on a better note would help.” — Quarterback Jay Cutler.

“We’re not playing well enough in all three phases to win on a consistent basis. ” — Coach Marc Trestman.

What we learned about the Cowboys:

1. These are not the Cowboys of the recent past. They do not have to depend on Tony Romo’s arm, instead sticking to the run with DeMarco Murray, getting themselves into third-and-manageable situations, and controlling the clock and the game. Murray might have had a 200-yard night if he hadn’t gotten himself into a couple of big losses trying to salvage plays.

2. Murray is a real horse. It is very rare for a back to handle the ball more than 40 times in a game, but he did that, and he was able to avoid tacklers as well at the end of the game as he was at the beginning. If he maintains his per-game rushing average, he would finish with 1,977 yards.

–RB DeMarco Murray has 1,998 yards from scrimmage this season, rushing and receiving combined. That is 40.6 percent of the Cowboys’ total offense. If he continues on his current pace, Murray would finish with 2,459 yards, which would be the second-highest total in NFL history. The record, 2,509, was set by RB Chris Johnson with Tennessee in 2009.

–Passer rating is often an imperfect statistic, but in QB Tony Romo’s case, it is a fair reflection of what appears to be his best season. His season passer rating, 108.8, is a career high, and he appears headed for only his second season above 100 (102.5 in 2011). What is more significant is that Romo’s back problems do not seem to be bothering him at all. He is moving well in the pocket and escaping pressure. He also has an impressive 25-to-8 touchdown to interception ratio.

–WR Dez Bryant finished the night with six receptions for 83 yards. Bryant has a double-figures total of touchdown reception for the third year in a row, though he did not score Thursday for the second game in a row. He has 50 touchdown catches in five NFL seasons.

What we learned about the Bears:

1. Chicago is likely to have a poorer record than the previous season for the second year in a row, and that is not a healthy prescription for coach Marc Trestman. He has two years remaining on his four-year contract, and the Bears historically are patient with coaches. They should be in this case, because he inherited a defense in need of retooling, and the offensive line has struggled because of injuries.

2. The defense is awful. (Then again, we already should have known that.) This may be the most damning of all the statistics: The Bears have punted 16 times more than their opponents this year while also being a minus-6 in turnover margin. Those numbers do not add up to winning football.

–In the category of statistics can be deceiving, QB Jay Cutler has a 91.7 passer rating this year. That would be the highest of Cutler’s career. However, the figure is inflated by a lot of yardage Cutler piled up in garbage time of lopsided defeats, such as Thursday night against Dallas. In the fourth quarter, he completed 16 of 22 passes for 183 yards. Unfortunately for him, the Bears were behind 35-7 when the fourth quarter began.

–The loss of WR Brandon Marshall would be a significant one for a struggling Chicago offense if Marshall’s rib injury, sustained Thursday against Dallas, proves serious. He made a 42-yard circus catch on a second-quarter touchdown drive before being hurt. Marshall finished the night with three catches for 61 yards. The Bears have only one other reliable wideout, Alshon Jeffery, although RB Matt Forte and TE Martellus Bennett rank No. 1 and 2, respectively, on the team in catches.

–DE Jared Allen, a big-money signee in April, was slow to get going this season, and he has just five sacks on the season. He was credited with half of the only Chicago sack against Dallas QB Tony Romo on Thursday. Allen will have to hustle to extend his streak of seven consecutive double-digit sack seasons.