Drummond had 10 points and 11 rebounds, but was disappointed New Orleans established itself as better team near the basket.
"It's on Greg and I to figure it out. We can't continue to let guys come in our paint and do those kinds of things to us," Drummond said. "It's a building process and we're going to figure it out. It's not going to happen for too long."
Detroit had one last lead when Jennings stole the ball from Holiday and heaved the ball down-court to Monroe for a fast-break dunk to make it 103-102. That's when Anderson responded with his second 3 of the extra period to give New Orleans the lead for good.
"We lost track of him in overtime," Monroe said of Anderson. "With a guy like that, you can't give him one second to get that shot off. ... We did a good job most of the game, but he hurt us in overtime."
Detroit trailed 108-106 after Jennings' floater off the glass with 13 seconds left. Detroit then fouled Evans, who missed his second free throw, but Josh Smith was called for a lane violation, and Evans hit on his extra chance to seal it.
The Pelicans led by as many as 12 points in the third quarter when Holiday's 15-foot pull-up made it 83-71, but that lead evaporated when Stuckey's turnaround jumper late in the period began a 12-0 Detroit run that included Monroe's layup and putback.
Detroit finally tied the game at 96 on Josh Smith's running hook with 1:19 left. Both teams then went cold, each failing to score on a pair of possessions, and the game went to overtime after Jennings missed two jumpers in the final seconds.
NOTES: Eric Gordon scored 14 for New Orleans. ... Smith scored 11 for Detroit. ... The Pistons rested Chauncey Billups in what was the Pistons' second game in as many nights, while Stuckey returned from a two-game absence cause by left knee soreness.