NEW ORLEANS — Call it heavenly redemption.

Last season in the Mercedes-Benz Superdome, San Francisco 49ers linebacker Ahmad Brooks was flagged for a fourth-down hit to the head of quarterback Drew Brees that gave the New Orleans Saints new life and fueled a 23-20 comeback victory.

But on Sunday in overtime, Brooks slammed into Brees from the blindside, forcing a critical fumble at the Saints’ 17-yard line that set up Phil Dawson for a 35-yard field goal with 5:14 left that gave the 49ers a wild 27-24 victory over the Saints, snapping a two-game losing streak and ending New Orleans’ 11-game home winning streak.

“I thought it was a tremendous performance,” said 49ers coach Jim Harbaugh. “This is a tough place to play and a tough team to play against. It was great team defense, but also great individual performances as well.”

As big as Brooks’ sack and forced fumble was, the critical play of the game may have come in the final minute of regulation. Trailing 24-21, quarterback Colin Kaepernick (14 of 32 for 210 yards and one TD) faced a fourth-and-10 from the 49ers’ 22 and was pressured out of the pocket to right.

Kaepernick reached the sidelines before wheeling to throw a 51-yard strike across the field to wide receiver Michael Crabtree, who had slipped 20 yards behind cornerback Corey White on the left side.

That gave the 49ers a first down at the Saints’ 27, and three incompletions later, Dawson came on the hit the tying field goal.

“The play got extended,” Saints coach Sean Payton said. “It was a broken play. The coverage areas are good for three or four seconds, but then everyone scattered to different spots. All of a sudden, it’s seven or eight seconds and it’s hard to keep your coverage integrity.”

In overtime, the Saints won the toss but were forced to punt after moving to midfield. The 49ers moved the ball to the Saints’ 43-yard line before Kaepernick was sacked on third down by linebacker Ramon Humber.

After getting the ball back, Brees faced a second-and-15 from the Saints’ 15. Looking deep initially, Brees double-clutched and couldn’t get the ball out quickly enough, allowing Brooks to bat the ball from his hands.

“We had a vertical route called, but I came back down to the check-down (for running back Travaris Cadet),” Brees said. “There was nobody around him, and I think he could’ve run forever. Unfortunately, I got hit and the ball came out.”

Linebacker Chris Borland recovered for the 49ers at the 17, and Harbaugh wasted no time sending in Dawson to kick the game-winner.

Despite completing 28 of 47 passes for 292 yards and three touchdowns — two to tight end Jimmy Graham for 11 and 2 yards in the second half — Brees had his troubles with the San Francisco defense.

Brees was picked off twice in the first half, one of which set up a point-blank touchdown drive for the 49ers, capped by Frank Gore’s 4-yard run.

The second interception was the result of rare bad decision by Brees, who threw into triple coverage trying to squeeze in a touchdown pass to Graham late in the half. Cornerback Chris Culliver easily made the interception in the end zone, and the 49ers led 21-10 at halftime.

The Saints had one desperation attempt to win it at the end of regulation, but Graham was called for pushing off against cornerback Perrish Cox on his 47-yard Hail Mary catch, and the game went to overtime.

What the 49ers said:

“Somebody needed to make a play. We said that in the huddle — ‘Somebody needs to be great’ — and Ahmad (Brooks) did it. We watched the film this week of him coming around the corner (last year) and almost taking Drew’s head off. He was able to make that play (today).” — Safety Antoine Bethea

What the Saints said:

“We’ve lost two games in overtime (Atlanta and San Francisco) where the offense turned the ball over in our own territory. We really never gave our defense a chance. They just brought the field goal unit out. That’s obviously something we can’t do. I just feel like the teams we’ve played against have just made more plays than us.” — Quarterback Drew Brees

What we learned about the 49ers:

1. The 49ers had struggled the last three games trying to get their running game going, and they made a concerted effort to do that against the Saints. Frank Gore got 23 carries for 81 yards — just a 3.5-yard average — but it kept the Saints’ defense at home. Carlos Hyde (4 carries for 36 yards) came in with fresh legs in overtime and ripped off a 15-yard gain. The maligned offensive line blocked well.

2. Despite its recent struggles, San Francisco (5-4) is a tough out on the road. The victory over the Saints gave Jim Harbaugh a 20-9 record on the road in the last 3 1/2 seasons. They did it by forcing three Saints’ turnovers and giving up just one. Antoine Bethea’s first-quarter interception of Drew Brees turned into a 19-yard TD drive.

–Rookie LB Chris Borland, starting for injured Patrick Willis, continued his superb play, leading the 49ers with 17 tackles, including 11 unassisted. Borland had two tackles for loss and recovered the fumble caused by LB Ahmad Brooks in overtime.

–WR Anquan Boldin was a force with six catches for 95 yards, including a 15-yard TD reception on a fade route in the second quarter. But he also had four or five drops to blunt what could have been a monster game. One of his drops near midfield might have gone for an 85-yard score.

–LB Ahmad Brooks never gave up in his pursuit of Drew Brees, making the key play of the game in punching the ball out in overtime to set up Phil Dawson’s winning field goal. “I was really surprised he held the ball as long as he did,” Brooks said. “I was rushing and turning the corner nd thinking to myself, ‘Dang, is he going to throw the ball yet?’ But he didn’t, and I was able to make a play.”

What we learned about the Saints:

1. Turnovers kill. The Saints entered the game minus-6 in takeaways, and they shot themselves in the foot again, with Drew Brees throwing two interceptions and losing a critical fumble in overtime. They are now minus-8 on the season.

2. Running back Mark Ingram is playing extremely effectively as he seeks a long-term contract from the Saints after this season. He rushed for 120 yards on 27 carries — his third consecutive game of at least 100 yards rushing.

–TE Jimmy Graham looks completely healed from a right shoulder injury he suffered four weeks ago, catching a game-high 10 passes for 76 yards and two scores. He almost made the most incredible play of the season at the end of regulation — a 47-yard game-winning TD catch on a Hail Mary — but he was called for pushing off against cornerback Perrish Cox before going up in the end zone for the ball.

–Rookie WR Brandin Cooks is starting to feel it. Early in the season he was used mostly on bubble screens and quick slants, but he went deep for a 31-yard touchdown catch in the first half.

–QB Drew Brees has now thrown 10 interceptions in nine games, not a comfortable feeling. “At the quarterback position, you understand there’s going to be moments for whatever reasons — bad decisions, bad throws, bad luck — that turnovers happen,” Brees said. “Sometimes they come in bunches. But you’ve got compartmentalize that and move on to the next play and do what you’re coached to do.”