The Spurs, who led by as many as 18 in the first half, left the door open in the tight closing stages, making just four-of eight from the free-throw line in the final two minutes.
Detroit pulled within 104-103 on a pair of Jodie Meeks free throws with eight seconds to play.
After a 20-second timeout, Spurs veteran Tim Duncan threw an inbound pass behind team-mate Patty Mills -- the Spurs 17th turnover of the game -- and Jennings banked in a shot at the other end to lift the Pistons to their sixth straight win.
The Spurs had won two straight after a disappointing December that saw them post a losing record for the month.
They welcomed back French point guard Tony Parker, who had missed 13 of the last 16 games with a hamstring injury.
But Parker, who sat out the Spurs' previous five games, had a quiet night upon his return, playing just under 13 minutes and scoring three points with two assists and two turnovers.
"It's disappointing," Spurs coach Greg Popovich said.
"I thought they out-competed us in the third quarter," added Popovich, whose team was out-scored 33-19 in the third period.
Andre Drummond led the Pistons with 20 points and 17 rebounds. D.J. Augustin added 19 off the bench, and Greg Monroe contributed a double-double of 17 points and 11 rebounds.
Cory Joseph's 16 points off the bench led the Spurs, who will try to regroup by Friday, when they host Phoenix.
The Suns opened a four-game road-trip on Tuesday with a 102-96 victory at Milwaukee.
source: www.abs-cbnnews.com
