J.J. Redick added 19 points for the Clippers, who have won consecutive games for the first time since Feb. 5-8 when they won three in a row on the road.
Brook Lopez had 25 points and 10 rebounds for Brooklyn, which was going for its first three-game winning streak of the season. Instead, the Nets lost their fifth straight to the Clippers at Staples Center.
Crawford carried the Clippers in the fourth, which began with them clinging to a two-point lead. He helped them open their first double-digit lead of the game on a jumper that made it 97-86.
Twice in a row, Paul fed DeAndre Jordan, who converted alley-oops into monster jams. They teamed up again for the same play on the Clippers' final basket. Jordan had 10 points and 10 rebounds.
The Clippers' defence got stops, too, and the Nets twice turned the ball over on offensive fouls.
Brooklyn outscored the Clippers 16-4, including seven by Bojan Bogdanovic, to lead by six late in the third. Los Angeles answered by scoring the final eight points to take an 81-79 lead into the fourth after Crawford's pull-up jumper beat the buzzer. Bogdanovic finished with 19 points.
The Clippers trailed by eight to start the game and found themselves in a back-and-forth throughout the first half. Neither team led by more than eight, and there were 12 ties and nine lead changes. Led by seven points from Paul, the Clippers closed on a 15-6 run to lead 52-46 at the break.
Nets: They haven't won three straight road games since March 21-April 1, 2015. ... They are 2-5 in leap day games.
Clippers: They swept the season series for the first time since 2007-08. ... They are 22-7 without injured Blake Griffin. ... Reserve G Austin Rivers, out with a left hand fracture, will be re-evaluated Tuesday. He could possibly return the next day. ... Team owner Steve Ballmer introduced a new mascot at halftime named Chuck, a California condor with a pink head, a large blue nose and a grey body. Ballmer promised fans a pair of red Converse sneakers if he dunked, and using a trampoline, the owner successfully did using both hands. ... A fan hit a halfcourt shot in the fourth quarter to win a new Jeep.
Nets: Visit the Lakers on Tuesday night. The Nets lost the first meeting 104-98 on Nov. 6.
Clippers: Host Thunder on Wednesday night. The Clippers lost by one point in the first meeting on Dec. 21.