Wade was called for a technical after tangling with Ryan Hollins and then he missed a jumper over Hollins on Miami's last shot of the third.
The Clippers' roll continued into the fourth, with Eric Bledsoe scoring their first eight points for a 93-76 lead. Griffin and Paul were on the bench, giving the second unit its chance to dominate the offense against Miami's starters. Bledsoe finished with 12 points and Caron Butler had 15.
"That's the first time I've been able to sit on the bench and almost be a fan," Griffin said. "It's fun to watch."
Griffin and Paul returned after Miami cut its deficit to 104-93 with 3:47 remaining. But it was only for insurance as the Heat failed to make a serious run in the closing minutes.
"The road just gets tougher," Heat coach Erik Spoelstra said. "That's a good team. We view them as legit competitors for the title.'"
Miami led 54-52 at halftime. James wasted no time asserting himself with a driving dunk 12 seconds into the game. The Clippers answered with eight straight points, the biggest run either team managed in the half.
Both teams put on a riveting display of dunks, 3-point shooting and power moves. The crowd cheered when Bledsoe blocked Wade on his way to the basket and then Norris Cole airballed a 3-pointer after the Heat recovered the ball.
"I turned it over so I just tried to get the ball back," Bledsoe said.
NOTES: Both teams had 19 turnovers. ... Wade hurt his foot in the third quarter of Monday's game at Houston when he stepped on teammate Chris Bosh. Against the Clippers, Wade stumbled out of bounds in the fourth quarter and went down after getting caught on one of the referees. ... Crawford has 164 points off the bench, making him the highest scoring reserve in the league this season. ... The Heat are 13-12 on the road all-time against the Clippers. ... The teams meet once more this season in Miami.