PITTSBURGH — The Pittsburgh Steelers picked the right time to get hot in an otherwise up-and-down season. As a result, they are headed to the playoffs.

The Steelers won their third straight game Sunday as quarterback Ben Roethlisberger shook off a knee injury and threw for 220 yards and a touchdown to help the Steelers clinch a playoff berth with a 20-12 victory over the Kansas City Chiefs on Sunday.

The Chiefs (8-7) had their playoff hopes severely damaged while losing for the fourth time in their last five games. Kansas City has to beat San Diego Chargers at home next Sunday and also hope for help from other teams in order to reach the postseason.

Through six games, the Steelers were just 3-3, and their playoff hopes were still in doubt when they fell to 7-5 with a loss to New Orleans on Nov. 30. However, they are 3-0 in December.

“The big thing is that we’ve evolved throughout,” Steelers coach Mike Tomlin said. “We were young at the early stages of the year. Same guys but they’ve matured through the process.

“We’ve been doing what teams need to do this time of year which is ratcheting it up and being a more difficult team to beat. We’re beating ourselves less which is good.”

The Steelers (10-5) can win the AFC North title next Sunday when they host the Cincinnati Bengals (9-4-1) in the regular-season finale. The Bengals host Denver on Monday night.

“Winning the division would mean everything,” Steelers wide receiver Antonio Brown said. “To bring the playoffs to Pittsburgh, to our fans, would be a great opportunity.”

Roethlisberger completed 18 of 25 passes in helping the Steelers (10-5) to the playoffs for first time since 2011 following back-to-back 8-8 seasons.

Quarterback Alex Smith had his first 300-yard passing game since 2012 — finishing with 311 — but he was sacked six times, and all of the Chiefs’ points came on four field goals by rookie kicker Cairo Santos.

“I thought the guys played hard and aggressive but we have to play more consistent football,” Chiefs coach Andy Reid said. “We can learn from this. We’re going to do that. We’re going to make sure we’re a better football team. That’s what we’ll do and whatever happens, happens.”

Roethlisberger injured his right knee when hit while throwing a 3-yard touchdown pass to Brown that gave the Steelers a 17-6 lead with 34 seconds remaining in the third quarter.

Roethlisberger was taken to the locker room for examination by the team’s medical staff while backup quarterback Bruce Gradkowski began warming up. However, Roethlisberger quickly returned to the sideline and went back into the game when the Steelers regained possession following a 43-yard field goal by Santos with 10:18 left that drew the Chiefs within eight points, 19-7.

Roethlisberger said he was “fine” after the game.

but wasn’t celebrating the victory

“We still have another game,” he said. “It’s a divisional game and it’s at home so we’re not looking past that.”

What the Steelers said:

“It’s going to be good to be back in the playoffs after missing for a couple of years, but that’s in the future. We have another big game next week (against Cincinnati for the AFC North title) and we’ll approach it as such.” — TE Heath Miller.

What the Chiefs said:

“It certainly makes things more difficult from how it was, but we have a lot of character inside our locker room and I don’t think it will impact our preparation on how we go about this next week.” — QB Alex Smith, on his team losing control of its playoff fate with the loss.

What we learned about the Steelers:

1. A young defense that was so porous and undisciplined throughout the first three months of the season is starting to finally pick up veteran defensive coordinator Dick LeBeau’s schemes. The Steelers were at their best on that side of the ball Sunday as they stuffed Jamaal Charles, sacked quarterback Alex Smith six times and held the Chiefs without a touchdown.

2. Linebacker James Harrison continues to sip from the fountain of youth at 36 after being coaxed out of retirement three weeks into the season. Harrison sat out the previous two games with a knee injury but returned to spearhead the Steelers defense with seven tackles, 1.5 sacks and two quarterback hurries.

–QB Ben Roethlisberger shook off a knee injury and threw for 220 yards and a touchdown. Roethlisberger completed 18 of 25 passes and was injured while throwing a 3-yard TD pass to WR Antonio Brown with 34 seconds in the third quarter that put the Steelers ahead 17-6. Roethlisberger was taken to the locker room for examination by the team’s medical staff while backup QB Bruce Gradkowski began warming up. However, Roethlisberger quickly returned to the sidelines and went back into the game when the Steelers regained possession following a 43-yard field goal by Kansas City K Cairo Santos with 10:18 left that drew the Chiefs within eight points. Roethlisberger then led the Steelers on a 12-play, 70-yard drive that culminated in a 23-yard field goal by K Shaun Suisham with 4:04 to go that increased their lead to 20-9. Roethlisberger raised his team-record passing yardage total to 4,635 yards, and he needs 365 yards against Cincinnati in the season finale next Sunday to reach 5,000. Roethlisberger’s 30 touchdown passes are two off his career high of 32 in 2007.

–WR Antonio Brown had a season-low 72 yards on seven receptions but scored his 12th touchdown of the season and broke his own franchise single-season record for receiving yards by raising his total to 1,569. He had 1,499 last season. Brown’s 122 receptions are also a team record. He is the fourth Steelers receiver to have a dozen TD receptions in a season, joining Buddy Dial (1961), Louis Lipps (1985) and Hines Ward (2002).

–RB Le’Veon Bell was held to 63 yards on 20 carries a week after Atlanta limited him to 47 yards on 20 carries. However, Bell put the Steelers ahead for good 10-6 when he scored on a 1-yard run in the second quarter. That gives him eight touchdowns in his last five games.

–SS Troy Polamalu (knee) sat out for the fourth time this season. He played in the last three games after missing the previous three.

–LB James Harrison returned to action after missing the previous two games with a knee injury. Harrison had seven tackles and a 1.5 sacks as the Steelers limited the Chiefs to four field goals.

What we learned about the Chiefs:

1. Star running back Jamaal Charles looks really banged up. Hampered by knee and ankle injuries along with being a week removed from suffering a concussion, Charles lacked explosiveness as he rushed for just 29 yards on nine carries and caught five passes for 48 yards. Aside from a 10-yard run, he managed just 19 yards on his other eight carries.

2. The Chiefs should strongly consider taking a wide receiver in the first round of the draft as they have yet to get a touchdown from that position through 15 games this season. Dating to last season, the streak is 18 games, the longest since the AFL-NFL merger in 1970. Perhaps Albert Wilson could be an answer to the problem as the undrafted free agent from Georgia State had five receptions for 87 yards both career highs.

–QB Alex Smith threw for 311 yards, completing 31 of 45 passes, but also was sacked six times. It was Smith’s first 300-yard passing game in his two seasons with the Chiefs and his first since Oct. 7, 2012, when he had 303 yards for San Francisco against Buffalo.

–WR Dwayne Bowe was in the starting lineup after being unable to practice all week because of illness. He caught six passes for 57 yards while being targeted a team-high eight times.

–WR Donnie Avery was an inactive despite not being on the injury report during the week. Avery, who has played only once since Week 4, has a lingering groin injury.

–DT Tamba Hali (knee) wound up playing after his status was in doubt when he missed practice Thursday and Friday. He had six tackles but seemed a step slow in the pass rush.

–CB Phillip Gaines left the game in the first quarter because of illness and did not return. The rookie was not feeling well before the game but was hopeful he could make it through the game.

–G Zach Fulton suffered a sprained foot. The rookie has started all 15 games this season.