Paul worked his offensive magic throughout the second half. He hit timely baskets to put the Clippers ahead and counter efforts by the Utah Jazz to rally.
The veteran guard also kept his composure during timeouts late in the fourth quarter and offered a steadying voice when his teammates needed one.
It added up to a 98-93 Game 6 win on Friday night. The Clippers survived for another game and now their Western Conference first-round series is tied 3-3.
Game 7 is scheduled for Sunday in Los Angeles.
"We've been in these situations time and time again since we were kids playing AAU," Paul said. "We've been in that situation in high school basketball and college basketball. It's the same game, there's just a lot more people at the game. You just go out there and try to stay in the moment."
Paul scored 29 points to lead the Clippers. DeAndre Jordan added 13 points and 18 rebounds. Luc Mbah a Moute and Austin Rivers scored 13 points apiece and Jamal Crawford added 12 points to lead the Clippers.
Los Angeles won a postseason game while Blake Griffin was sidelined with injury for the first time after going 37 of 75 (49.3 percent) from the floor.
Utah didn't go down without a fight. The Jazz rallied from a double-digit deficit and closed the gap to 96-93 with 43.6 seconds remaining after Gordon Hayward took a steal in for a dunk and then buried a 3-pointer off a Clippers turnover.
With Los Angeles clinging to a three-point lead, Joe Johnson had a chance to tie it for Utah in the closing seconds but missed a 3-pointer with 3.9 seconds remaining.
Paul hit two free throws with 1.0 second left to clinch the win.
"We had a great opportunity tonight to close it out and move to the next round," guard George Hill said. "That's the hardest thing to do is close teams out, especially when they're desperate."
Hayward scored 31 points and Hill added 22 to lead Utah. Rudy Gobert chipped in 15 points and nine rebounds for the Jazz. Utah ultimately could not overcome 7-of-26 shooting from 3-point range.
The Jazz also struggled with Jordan. He proved much more effective at crashing the boards and getting second-chance points than in the previous two games. Jordan also clogged the interior enough to force Utah to the perimeter for contested shots.
Jordan played 22 of 24 possible minutes after halftime.
"In the playoffs, your energy level is just up, so you don't think about how many minutes or plays," Jordan said. "You think about each possession and how important it is for our team. I'm just really taking whatever they give me."
Utah led through much of the first quarter after running off nine straight points -- punctuated by a Hayward dunk - to take a 9-3 lead. The Jazz went up 22-13 behind back-to-back baskets from Hayward and Derrick Favors.
Los Angeles answered with an 11-0 run, fueled by back-to-back baskets from Mbah a Moute. The Clippers finally took a 24-22 lead early in the second quarter on a layup from Marreese Speights.
Utah regained a 36-31 lead later in the second quarter after Gobert sank two free throws to finish off a 6-0 spurt. The Clippers quickly tied it up again on back-to-back baskets from Paul and tied it three more times before taking a 47-45 halftime lead on two free throws from Jordan.
"We got really good looks early in the game and didn't make them," Utah coach Quin Snyder said. "I thought we got a little stagnant when they were scoring. I don't think we were forceful enough with our attack."
Los Angeles used a 13-2 run to surge ahead 69-61 late in the third quarter. The Clippers took the lead on three Paul free throws, and Crawford drove for back-to-back layups to finish off the run. Paul later drilled a 3-pointer to give the Lakers their largest lead in the quarter at 74-63.
Once ahead by double digits, the Clippers stayed in front. Utah cut the lead to 80-74 on a second-chance 3-pointer from Raul Neto. Los Angeles squashed a potential run with baskets from Mbah a Moute and Paul and carved out a 91-77 lead on a 3-pointer from Rivers with 3:58 left.
Clippers coach Doc Rivers credited Paul with being equal to the task when Los Angeles needed a lift at critical junctures late in the second half.
"He is as competitive of a human being that I've ever been around," Rivers said. "When you put that with the talent and the will, that's why he has performances like this in big games."
NOTES: Utah outscored Los Angeles in the paint 26-14 in the first half. ... The Clippers had a 15-8 edge in second-chance points in the first three quarters but were outscored 8-0 in the fourth. ... Jazz F Gordon Hayward and Jazz G Rodney Hood shot a combined 3 of 15 on 3-pointers. ... Clippers G Austin Rivers shot 50 percent from the field (5 of 10) after going 0 of 4 in Game 5.