NEW ORLEANS — Running back Khiry Robinson plowed 18 yards over left guard for a touchdown to lift the New Orleans Saints to a 37-31 overtime victory over the Tampa Bay Buccaneers Sunday at the Mercedes Benz Superdome.

Robinson’s scoring run left two Bucs defensive backs — safeties Bradley McDougald and Mark Barron — pounding the turf in frustration at the Tampa Bay 5.

The Saints (2-3) trailed 31-20 with 13:28 left but scored the final 11 points of regulation to force overtime. They won despite a subpar performance by quarterback Drew Brees, who completed 35 of 57 passes for 371 yards but was picked off three times. The Saints also overcame 15 penalties against them for 113 yards. For the season, New Orleans has been penalized 42 times for 318 yards.

Despite having to settle for field goals of 30 and 29 yards by Shayne Graham on two first-quarter trips into the red zone, the Saints led 13-0 when Brees connected on a 15-yard screen pass to running back Pierre Thomas with 10:14 left in the second quarter.

The scoring pass was a perfect call on third-and-12, beating the Bucs’ all-out blitz with a toss to the left, and Thomas weaved his way through traffic for the score.

The Bucs then ran off 24 consecutive points, starting innocently enough, with a 55-yard field by rookie place-kicker Patrick Murray.

The Bucs took advantage of the first of several bad decisions by Brees, who was flushed from the pocket by defensive tackle Gerald McCoy and tried to squeeze a sideline pass to running back Travaris Cadet. Instead, cornerback Johnthan Banks wrestled the ball away from Cadet for an interception, setting up the Bucs at the Saints’ 40.

Four plays later, Bucs quarterback Mike Glennon cut the deficit to 13-10 with a 20-yard pass to wide receiver Louis Murphy in the left corner.

Tampa Bay took its first lead, 17-13, by driving 80 yards on seven plays with the second-half kickoff. The drive was kept alive by an illegal, third-down hit to Glennon’s helmet by defensive end Junior Galette. Running back Bobby Rainey’s 9-yard scoring run came as the result of a huge hole on the right side.

It only got worse for Brees. Under heavy pressure, Brees threw a wild pass that looked more like a shot-put heave, and the pass was easily picked off by linebacker Danny Lansanah, who rumbled 33 yards for a touchdown, putting the Bucs up 24-13 with 11:20 left in the third quarter.

New Orleans got the touchdown back with a 63-yard, 12-play drive, drawing within 24-20 on Brees’ 5-yard pass to Cadet on the left side.

But Tampa Bay answered with an 81-yard, 10-play march. Glennon made the key play after getting flushed from the pocket and appearing to head out of bounds. But at the last moment, Glennon turned and fired an across-field pass over the middle, which wide receiver Vincent Jackson hauled in for a 34-yard gain the New Orleans 10.

Glennon then hit rookie receiver Robert Herron for a 9-yard score, putting Tampa up 31-20 with 13:28 left.

Brees responded with a 78-yard drive that culminated with a weaving 23-yard TD run by Thomas, making it 31-26 with 9:28 remaining. Brees’ attempt at a 2-point conversion failed when tight end Benjamin Watson was stopped at the 1-yard line by cornerback Alterraun Verner.

The Saints, however, got the two points on the Bucs’ next series. On third-and-29 from the Tampa Bay 1, Galette took an inside move to sack Glennon for a safety with 6:44 left, and the Saints were within three, 31-28.

The Saints took over after the free kick at their 40-yard line, and Graham’s 44-yard field goal with 2:30 remaining tied it at 31, setting up overtime.

NOTES: Brees became the fastest quarterback to throw for 40,000 yards, surpassing the mark in 132 games. Dan Marino of the Miami Dolphins had been first in that category, accomplishing the mark in 153 games. … Saints’ tight end Jimmy Graham injured his right shoulder early in the second quarter and did not return. Graham had two catches for 36 yards. … On Tampa Bay’s three consecutive TD drives, QB Mike Glennon was 11-for-14 for 123 yards.