Griffin picked up two quick fouls early in the overtime period, and fouled out with 32 points and 10 rebounds. Dudley was 0-for-6 from the three point line, launched a clutch three pointer with 38 seconds left that gave the Clippers the lead for good.
Paul knocked down five out of six free throws that also sealed the victory.
Kevin Love finished with a MVP type performance with 45 points and 19 rebounds in the loss for Minnesota.
"We just blew it. Blew the game! I don't know how else to say it. We blew the game," Love said.
After a very tight battle between in the two teams in the opening quarter, Blake Griffin made his presence known on both ends of the floor in the second quarter. Griffin scored 20 points, and push the Clippers to a 56-54 halftime lead.
With 56 seconds left in the third quarter, Matt Barnes was called for a flagrant foul 2 on a defensive play against Kevin Love. Love scored five straight points in that one possession.
"I don't think it was flagrant 2..at all," said head coach Doc Rivers. "I didn't fully see it, but it shouldn't have been a flagrant 2 call."
The Clippers fought back and down 106-102 in the fourth quarter, the defense turned up a notch when Jamal Crawford dunked after Paul forced Kevin Martin to turn the ball over. With the game tied, Timberwolves center Nikola Pekovic had two opportunities to win the game, and missed both shots.
Once again the win came down to Pekovic making a shot and missed a five footer, Paul was fouled where made two free throws that won the game in overtime.
We need to know how to win and play hard all the way to the end," Pekovic said. "Winning is a habit, like everything else. We still need to get over the hump to learn how to close out these games."
Nikola Pekovic finished with 34 points and 14 rebounds in the loss.
Chris Paul finished with 19 points, 13 rebounds, and Jared Dudley added 15 points.
"Doc always said it's not over, and we just believed," said Paul. "I keep saying this in the huddle 'we play to win the game', over and over again."
The Clippers face another battle on Christmas Day, against the Golden State Warriors in Oakland.