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 defense 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.