Griffin scored 31 points, falling two points shy of becoming the first Clipper to score 10,000 points with the team. He hit 12 of 19 shots and added seven assists.
Paul had 29 points and 10 assists, and Jamal Crawford added 19 points for the Clippers, who won for the second time in as many nights and moved within one game of the idle Utah Jazz for fourth place in the Western Conference.
The Clippers (46-31) swept all four games from Phoenix this season and have won 13 of the last 15 meetings.
With Kentucky coach John Calipari in town for the Final Four and watching his former Wildcats from a courtside seat, Devin Booker had a game-high 33 points and nine assists before fouling out, and Tyler Ulis had 16 points and 13 assists.
But the Suns (22-54) lost their 10th straight game overall. Their 54 losses are the most in the West.
Phoenix missed 11 of 24 free throws, including four straight by TJ Warren in the final 2:29.
Phoenix rallied from 12 points down in the third quarter and tied the game twice in the fourth, the last time on a Booker layup with 7:52 left. But Griffin's 3-point play started a 7-0 run and when Booker fouled out with 4:45 left the Suns trailed 113-106.
But Ulis set up Marquese Chriss for two baskets between a bank shot of his own to cut the Los Angeles lead to 114-112 with 3:43 left. But that's as close as Phoenix got.
Booker and Chriss combined to make 10 of 14 shots in the first quarter and provided 23 of Phoenix's 35 points. The Suns shot 60 percent and Warren's tip-in with 10.4 seconds left gave them a 35-31 lead after one.
Griffin had eight points and Paul had seven for the Clippers, but they committed seven turnovers.
But the Clippers answered with 36 points in the second quarter, 12 of them by Griffin. The Clippers hit nine of 13 3-pointers in the first half (69 percent) and took their biggest lead when a Luc Mbah a Moute 3-pointer put them up 67-59 with 8.7 seconds left.
Los Angeles stretched its lead to 12 twice in the third period, the last time at 87-75 on another Mbah a Moute 3-pointer with 4:20 left. But the Suns scored the final nine points of the quarter and Warren's tip-in at the buzzer pulled Phoenix within a point at 93-92.
NOTES: Suns G Leandro Barbosa (right hamstring spasm) missed his third straight game. Phoenix signed F Jarell Eddie to a second 10-day contract on Wednesday and dressed 10 players for the game. ... Suns coach Earl Watson said he hopes to have F Dragan Bender (ankle surgery) back within the next week. ... Blake Griffin would be the second player in franchise history to reach the 10,000-point plateau, but Randy Smith scored 10,467 of his 12,735 career points with the Buffalo Braves before the team headed to San Diego. ... Suns G Devin Booker's 33 points give him 2,637 career points, passing Dwight Howard for the fourth-most points in NBA history before turning 21 years old. He trails only LeBron James (4,649), Kevin Durant (3,495), Carmelo Anthony (3,283) and Kobe Bryant (2,755).