Trailing 54-52 at the game's midway point, the home team rocked the Heat's 'Big Three' of LeBron James, Dwyane Wade and Chris Bosh, building a 20-point lead before fending off a late Miami rally to complete their fourth straight win.
Point guard Paul marshalled the Clippers superbly with 16 points and 10 assists in front of a sellout crowd of 19,000 at the Staples Center while twice All-Star forward Blake Griffin also had a double-double, with 20 points and 14 rebounds.
Jamal Crawford, the 2010 Sixth Man-of-the-Year when he was playing for the Atlanta Hawks, added 22 points off the bench to enhance his status as the highest scoring reserve in the league this season.
"We just got some big stops, came back and made some shots in the third quarter," Griffin said after the Clippers out-rebounded the Heat 38-36 while improving their win-loss record to 6-2 for the season. "Miami is a tough team.
"To have that kind of success in the second half, from both our first and second team, is a great thing. But we can't rest on a win like this. We can be even better."
James was a tower of strength for the Heat with a game-high 30 points and seven assists while veteran guard Ray Allen contributed 14 points and Bosh 11 but the visitors paid a price after being restricted to 45.5 percent shooting from the field.
"We lost it in the third quarter," said eight-time All-Star forward and last season's NBA Finals MVP James, who led his team's scoring with 12-of-23 shooting from the field.
"Chris (Paul) was making bombs, back-to-back threes, and Blake had a good quarter too. They started making free throws and we couldn't recover from that."
Heat coach Eric Spoelstra was fulsome in his praise for the Clippers after his own team slipped to 6-3 for the season.
"We view them as legitimate contenders for the title," he said. "We know and respect what these guys are about. They played a good game and beat us fair and square."
In a high-octane start, James and Griffin treated the crowd to a sizzling display of driving layups, dunks and jump shots before a late burst of scoring by Crawford put the Clippers ahead 25-24 after a tightly contested first quarter.
There were seven lead changes in the second period but a trio of three-pointers by backup forward Rashard Lewis helped the Heat take a narrow 54-52 advantage into halftime.
Roared on by the home crowd, the Clippers upped the tempo and forward Caron Butler sank a three-pointer midway through the third quarter to give his team a welcome 67-60 lead.
Though the Heat briefly closed the gap to one, five-time All-Star Paul lifted Los Angeles spirits with back-to-back three-pointers to put them ahead 80-72 as loud chants of 'CP3, CP3' echoed around the Staples Center.
Leading 85-74 going into the fourth quarter, the Clippers padded that advantage to 93-76 after backup guard Eric Bledsoe followed a pair of layups with two free throws.
A Crawford jump shot gave Los Angeles their biggest lead of the night at 104-84 and Miami were unable to close the gap, despite a furious late rally.
"It's a team effort every night," said Paul. "Everybody is working hard and playing together. I know they (the Heat) ended with 100 (points) but our defence in the second half is what got us the win."