NEW ORLEANS (AP) — The moment Garrett Hartley’s foot drove through the ball, the Louisiana Superdome crowd erupted and Saints owner Tom Benson raised his arms in triumph.

The presumption was that these Saints, in this magical season, were going to pull out another win in the clutch.

Not so fast.

Hartley’s 37-yarder hooked to the left, and those who’d allowed themselves to celebrate prematurely were sent home soon after in stunned silence.

Carnell Williams rushed for 129 yards and a score, and Connor Barth kicked a 47-yard field goal in overtime, lifting Tampa Bay to a 20-17 upset on Sunday that, for the time being, prevented New Orleans from securing home field throughout the NFC playoffs.

Even in what will go down as the best regular season in Saints history, a franchise long known more for its stumbles than success found a way to make history with a loss. According to STATS LLC, the result marked the first time a 13-win team lost to a team that came in with only two victories.

‘‘It’s hard to explain,’’ Saints quarterback Drew Brees said. ‘‘We started off fast, then after that there was a big lull.’’

Kind of like their season.

New Orleans (13-2) won nine of its first 11 games by double digits. After a 38-17 win over New England, the Saints appeared better situated than ever to make the franchise’s first run to the Super Bowl.

Since then, the Saints have pulled out a pair of three-point wins over non-playoff teams and have lost two straight — both at home — starting with a 24-17 setback to Dallas.

If Minnesota wins its final two games, starting Monday night in Chicago, the Saints will have to win in Carolina next Sunday to secure the franchise’s first No. 1 playoff seeding.

‘‘The fact is we need to play better,’’ Brees said. ‘‘I don’t feel like we’ve played our best football in a while and there’s definitely some things that need to be corrected.

‘‘You always find out more about a team when you start facing adversity. This is just yet another one of those situations that I feel we have the right character, the right type of leadership to bounce back from and help us become stronger going into the playoffs.’’

New Orleans was favored by more than two touchdowns over the Buccaneers (3-12).

New Orleans sped out to a 17-0 lead with its first three possessions, but the Bucs, who have refused to quit on the season, cut it to 17-3 on Barth’s 34-yard field goal as time expired in the first half.

‘‘We went back in the locker room and I tried to settle the guys down,’’ first-year Tampa Bay coach Raheem Morris said. ‘‘They believe in me and I believe in them. … I know this team is getting better. I could see it every week, even when we were losing.’’

Williams had not rushed for 100 yards since 2006 — before serious injuries in both knees. He scored on a 23-yard run in the fourth quarter, speeding away from pursuit once he broke into the open near the left sideline. Micheal Spurlock’s 77-yard punt return tied it at 17.

Hartley, who became the Saints’ lone place kicker last week when the Saints waived John Carney and made him a kicking consultant, said he rushed his missed kick.

‘‘Knowing I let my team down is the worst thing,’’ he said. ‘‘It’s definitely humbling. You have to learn from these experiences in order to prevail the next one.’’

After Hartley’s miss, only the second in his two-year career and first from inside 58 yards, Tampa Bay won the coin toss to open overtime and scored soon after.

‘‘It feels great to win two in a row,’’ Williams said. ‘‘This organization learned something today: that no matter how far down you are you can still get back up. And that’s what happened out here today. I am so proud of our offensive line. They did all the work and all I did was hit the holes.’’

The Bucs might have won in regulation if not for squandering two other scoring chances in the second half, once on Tracy Porter’s interception in the end zone and once on a failed fourth-and-short from the New Orleans 19-yard line.

Meanwhile, Tampa Bay’s defense continued to show improvement since Morris took charge of the group following New Orleans’ 38-7 win at Tampa Bay five weeks ago.

Brees was held to 258 yards passing and one touchdown. The Saints rushed for 124 yards, but gained only 28 yards on the ground in the second half, when leading rusher Pierre Thomas sat out with bruised ribs. Thomas had an 8-yard TD run for New Orleans’ first score. Robert Meachem’s 30-yard catch accounted for the second and was set up by Darren Sharper’s ninth interception of the season, during which he set an NFL record for interception return yards in a season with 376.

Bucs quarterback Josh Freeman was 21 of 31 for 271 yards. He did not throw a touchdown pass and was intercepted twice, but made a pivotal play in overtime when he scrambled for a first down on third-and-6, sustaining the winning drive.

Tampa Bay’s Kellen Winslow had four catches for 76 yards, including a 35-yard catch during a 98-yard drive that ended with Williams’ score.

NOTES: Buccaneers FB Earnest Graham was helped off the field favoring his right leg in overtime and DE Jimmy Wilkerson left the game under his own power with a knee injury. … Winslow has 828 yards receiving, breaking the single-season franchise record for tight ends that had been held by Jimmie Giles, who had 786 yards in 1981. … With their 17th point of the game, the Saints became the 12th team to score 500 points in a season in NFL history. The previous was the 2007 New England Patriots, who scored an NFL-record 589 points while winning all 16 regular-season games.