Paul, who finished with 19 points and a season-high 15 assists, canned the go-ahead jumper with 22.1 seconds remaining in overtime for Los Angeles.
The Clippers forced extra time when Blake Griffin tipped in a shot with 19.2 seconds left in regulation. He finished with 17 points.
The Pistons scored the first six points in overtime but couldn't maintain the momentum.
Greg Monroe scored six of his 23 points in overtime and grabbed 15 rebounds for Detroit.
Tayshaun Prince contributed 20 points in Detroit's losing effort.