Griffin was ejected for his second technical after scuffling with Andrew Bogut, following Green to the showers.
Paul's lay-in with 11.9 seconds left went around the rim and out, but Andre Iguodala missed a pair of free throws with 9.3 seconds remaining. That gave the Clippers the ball back with 8.3 seconds to go.
Stephen Curry overcame a slow start to score seven of his 15 points over the final 3:01 to go with 11 assists as Golden State snapped the Pacific Division-leading Clippers' season-best five-game winning streak. Thompson finished with 23 points and David Lee had 23 points and 13 rebounds.
When the game ended, players tangled near the tunnel to the Clippers' locker room and security personnel stepped in — and former Warriors swingman Jackson could be seen screaming in the fray.
Whether the Warriors intended to ignite Griffin, Rivers can only guess.
"I don't know if they were but it sure looked like it. I can't accuse them of that but it looked like it. I'm not sure but that's what it looked like," Rivers said. "It's whatever you have to do to win, I guess."
This one sure was feisty and festive from the opening tipoff at sold-out Oracle Arena, where fans wore "Christmas Whiteout" snowflake Warriors T-shirts for the holiday occasion.
Paul had 26 points and 11 assists as he and Curry put on a late-game show between two of the Western Conference's top point guards. Griffin added 20 points, 14 rebounds and five assists before his early exit.
Bogut added 10 points and 14 rebounds.
Both Rivers and Jackson said before the game this can't truly be a rivalry until both teams are consistent contenders year after year.
It's certainly getting testy enough to be close to such status. And they see each other twice more. The Clippers come back Jan. 30.