The teams entered the fourth quarter tied at 72.
Luckily for the Clippers, Jamal Crawford had a hot hand, scoring eight of his team-leading 25 points in the fourth quarter. That included a 21-foot jumper with 2 minutes 4 seconds left that gave the Clippers a five-point lead, 94-89.
It was a big win for the Clippers, who are in sixth place in the Western Conference, four games behind the second-place Trail Blazers.
The Trail Blazers, who hadn't led since the first quarter, took the lead in the fourth after C.J. McCollum made a running jumper with 10:15 left. Damian Lillard, who leads the league in points in the fourth quarter, had 12 of his 15 points then, but that wasn't quite enough to pull out the win.
Chris Paul had 23 points, 10 assists and six rebounds for the Clippers. Blake Griffin added 18 points and only three rebounds, and DeAndre Jordan had 17 points and 18 rebounds.
LaMarcus Aldridge led the Trail Blazers (30-9) with 37 points on 14-for-28 shooting from the field and 12 rebounds.
The Clippers (26-13) are now only a half-game behind the Dallas Mavericks for fifth place in the West.
Follow Melissa Rohlin on Twitter @melissarohlin