NEW ORLEANS -- Pierre Thomas kept his body compact and his thick legs churning, bursting through thin seams in the Tampa Bay defense, slipping away from some tacklers and surging through others.
Eight seasons after entering the NFL as an undrafted free agent, Thomas still comes up with the big gains on screen passes and on the ground that have been the hallmarks of his career.
Brees called Thomas "everything you'd want in a teammate in regards to not only his production on game day but throughout the week."
"He can do it all," Brees added. "He's one of the best all-purpose backs in the league, no question, and he's been that for a long time."
With a shoulder injury forcing tight end Jimmy Graham from the game in the second quarter, Brees still passed for 371 yards. But he also misfired 22 times, finishing 35 of 57.
Thomas became one of Brees' top targets, catching eight passes for 77 yards, including a 15-yard touchdown on a screen pass. He rushed for 35 yards, highlighted by his 27-yard touchdown run in the fourth quarter.
Robinson rushed 21 times for 89 yards. Thomas, Robinson and fellow running back Travaris Cadet combined for 228 yards from scrimmage and four TDs.
"We dug deep and did what we have to do to win," Thomas said. "We never gave up hope. We kept fighting, fighting and fighting. It shows how much heart we have."
The Buccaneers (1-4) hurt themselves with 15 penalties for 113 yards, none more damaging than the flag on cornerback Jonathan Banks in overtime for illegal hands to the face as Brees threw incomplete on third down.
The penalties "really hurt us," Bucs coach Lovie Smith said, adding that infractions like the one Banks committed "are ones you just can't make."
Starting for Josh McCown (injured thumb), Glennon nearly got his second straight victory in a stadium where the Bucs have not won since the last game of the 2010 regular season. That was also the last time the Saints lost in the Superdome with coach Sean Payton - who was suspended in 2012 - roaming the sideline.
The Saints cut it 31-26 on Thomas' rushing TD, then failed to convert a 2-point try. But with the Superdome crowd roaring, the Bucs' offense seemed to unravel. A holding penalty was followed by a botched snap, then a pair of pre-snap penalties that backed Tamp Bay up against its goal line.
"We were up five at the time and would have liked to have moved the ball and get points, but at least push them back so they didn't have great field position," Glennon said. "It was not well-executed by us and it's something we'll look at."
The series ended when Galette stunted inside behind defensive end Cameron Jordan's outside pass rush and had a free run at Glennon for a safety that made it a 31-28.
"I saw the opening and shot it," Galette said.
New Orleans then capped the next drive with Shayne Graham's 44-yard field goal to tie it with 2:30 left.
Brees responded with a 5-yard TD pass to Cadet, setting up a wild fourth quarter.
NOTES: In addition to Jimmy Graham, the Saints also lost C Jonathan Goodwin (knee) and LB Ramon Humber (ankle) to injuries during the game. ... The Bucs did not announce any injuries. ... Brees surpassed 40,000 yards passing with the Saints in his 132nd game with the club. Dan Marino had been the fastest to 40,000 yards with one club, doing so with Miami in 153 games.
Copyright 2014 by The Associated Press