Paul scored on a drive and made a free throw in the final minute of overtime, lifting Los Angeles to a 105-103 victory at Houston on Sunday night.
Neither team led by more than seven points, but Paul proved to be too much for the Rockets to overcome. The five-time All-Star point guard finished with 28 points and 10 assists.
The Clippers held the Rockets scoreless over the last 90 seconds, and Los Angeles beat Houston for just the eighth time in the last 33 meetings.
"Both teams made some big plays, but ultimately, we got some big stops to get us the win," Paul said.
"This was a win we needed," Griffin said. "It is a relief."
"Both teams were playing well," Martin said. "I think that's why it hurts the most. We have been harping over coming out and setting a tone, effort-wise. We did everything right, except for one thing."
The teams traded the lead six times over the final three minutes of the fourth quarter, and were tied at 97 in the closing seconds. Paul, guarded by Courtney Lee, let the clock wind down, but he couldn't get a shot off before the final buzzer, forcing overtime.
The lead changed hands three more times early in overtime before Lee beat the shot clock with a 3-pointer from the wing with 1:34 left to put the Rockets up 103-100.
Paul dished to Griffin for a powerful slam to cut the Clippers' deficit to one, then scored on a drive to put L.A. back on top with 51 seconds to go.
Kevin Martin missed a 3-point try, Kenyon Martin rebounded and Paul made a free throw with 4.9 seconds remaining for a 105-103 lead. Martin missed another 3-point try on Houston's final play.
"The shot was just off by about a centimeter," Kevin Martin said.
The Clippers outrebounded Houston 49-43 to make up for 16 turnovers. L.A. was outrebounded in its previous two games, and coach Vinny Del Negro made that a point of emphasis before Sunday's game.
"That was definitely something we need to control," Foye said. "We have to get in there and crash the boards."
Houston went 10 for 20 from 3-point range, but 37 for 86 overall.
"We had our chances in that game, so I'm not disappointed in our effort," Houston coach Kevin McHale said. "I just wish that when you have a team like that and you've got them on the ropes, you can't have any mistakes. We had a couple down the stretch, and it hurt us."
Griffin, shadowed by Scola early, missed his first three shots. Kevin Martin scored nine points and delivered four assists in the first quarter, and Houston led 30-25.
The Clippers rebounded better with Griffin on the bench for the first 6 1/2 minutes of the second quarter. DeAndre Jordan grabbed an offensive rebound and scored to put Los Angeles ahead 36-35 before Griffin returned.
Griffin swished a jumper from the wing a minute later, his first points. He was 1 for 6 from the field when he swept down the lane for a left-handed dunk to make it 40-all.
Dalembert scored 14 points and Kevin Martin had 12 in the first half, and Houston led 47-45 at the break.
Kyle Lowry drove for a layup early in the third quarter, collided with Jordan and landed hard on his left wrist. He stayed in the game and converted the resulting free throw, putting Houston up 55-52. Lowry took another hard spill and scored again a minute later, as Houston continued to attack the Clippers inside.
The Clippers went 10 for 13 from the free-throw line in the third quarter to build a small lead heading to the fourth.
Griffin has 22 double-doubles this season. ... Paul has a steal in 39 consecutive games, the NBA's longest active streak. ... The Rockets open a five-game road trip in Boston on Tuesday. ... The Rockets have been outrebounded in 10 straight games.