That's when Paul went to work, fighting off Tony Allen's defence as he tried to drive to the right baseline. Paul got there and put up a one-handed running jumper that went off the glass and through the net with a tenth of a second to go.
The Clippers won 93-91 on Monday night for a 2-0 lead in their first-round playoff series.
"That's why they're star players. They step up in the biggest moments," Clippers coach Vinny Del Negro said. "Chris has done it his whole career. In the biggest moments, that's usually when he's at his best. He has that competitive drive, which is a gift that not everyone has."
Allen was supposed to force Paul to his weaker left side, but it didn't happen.
"It could have gone either way. If he had missed, you could have been saying how good a defender I was," Allen said. "The guy made an amazing shot and all you can do is just deal with the results."
The Grizzlies have two days to think things over before Game 3 in Memphis on Thursday.
"It's not doom and gloom," Memphis coach Lionel Hollins said. "We got to go home and there's going to be two hard-fought battles."
Paul finished with 24 points and nine assists, Blake Griffin added 21 points and eight rebounds after fouling out of Game 1, and Jamal Crawford scored 15 points on the day he finished second to J.R. Smith of the Knicks for the league's Sixth Man of the Year award.
Mike Conley scored a career playoff-high 28 points for Memphis. Marc Gasol added 17 points, Allen had 16 points and 10 rebounds, and Zach Randolph had 13 points while saddled with five fouls for the second straight game.
"We had a chance to win the game," Hollins said. "We didn't get enough defensive stops and we missed too many free throws."
The Grizzlies were 23 of 34 from the line in the game, but just 6 of 10 in the fourth, when Conley led their charge with 10 points.
The Clippers' bench started the fourth and ran off eight straight points for the game's first double-digit lead, 81-71. Eric Bledsoe and Matt Barnes had four points each.
Conley answered with five straight points to close the Grizzlies within seven points.
Griffin and Paul joined the second unit, and Griffin scored on a driving dunk for an 85-76 lead. The Clippers returned to their high-flying ways after Lob City managed just one dunk in the series opener.
The Grizzlies tied the game at 89 on a three-point play by Darrell Arthur.
Paul carried the Clippers over the final 3:46, scoring eight straight points, including a basket that gave them a 91-89 lead with 1:20 to play.
Gasol tied it again when Conley found him alone for a dunk to make it 91-all.
"We thought we played as good a game as we could," Conley said. "It hurts. We wanted to come here and steal one."
Griffin won a hard-fought jump ball, but Paul missed a desperation 3-point attempt as the shot clock expired. He redeemed himself and set off a raucous reaction — with longtime Clippers fan Billy Crystal pumping both arms in the air — when he drove the right baseline against Allen and banked in the game-winner.
"We put our best defender on him and Chris was able to get around him going right," Conley said. "He just hit a tough shot."
Both teams stayed on the court while the referees reviewed Paul's shot. It was declared good, leaving Memphis a tick of the clock to inbound the ball but not enough to get off a final shot.
"C.P. made a tough, tough shot there off the glass," Memphis' Tayshaun Prince said. "It was great defence and things like that, but things never come down to the last play. It's what you do in the middle of the game that dictates winning or losing."
Memphis was outrebounded — 40-38 — for the second straight game, but not by double digits like in Game 1.
"The thing we're most disappointed in is Game 1, how we all just came out flat," Prince said. "We were just very flat as a group. The effort was a lot better today, but we have to be better."
NOTES: The Clippers have won nine in a row, including seven straight to end the regular season. ... The Grizzlies outscored the Clippers 20-18 in the fourth. ... The Clippers had a 50-46 edge in the paint, while Memphis held a 15-11 advantage on second-chance points.