Paul handed out 13 assists and Griffin had 10 rebounds and four steals for Los Angeles, which beat the Timberwolves for an eighth consecutive meeting and notched a fifth straight win overall.
Jamal Crawford scored two late baskets during a 6-1 run to end regulation as the Clippers staged a late rally to force extra time.
Crawford finished with 22 points and Darren Collison added 18 off the bench.
Kevin Love poured in 45 points on 15-of-23 shooting, hauled down 19 rebounds and distributed six assists for Minnesota.
Nikola Pekovic netted a career-high 34 points and grabbed 14 rebounds, but missed a potential tying jump hook shot with 5 seconds left in overtime.