Marc Gasol had 23 points, nine rebounds and eight assists to help put the Grizzlies (6-5) over .500 for the first time this season.
Mike Conley scored eight of his 15 points during a 4-minute span of the fourth quarter.
Blake Griffin had 23 points and 11 rebounds for the Clippers. Paul had 18 points and 11 assists for his 11 straight double-double, the most by any player from the start of a season since Magic Johnson in 1990-91.
Allen was charged with a flagrant-2 foul with 1:51 left in the opening quarter after he lifted his left leg in a vain attempt to impede Paul's drive to the basket and kicked him in the face. Allen walked over to Paul at the foul line to apologize while referees Bill Kennedy, Mark Ayotte and John Goble watched the replay at the official scorer's table to determine the severity of the foul.
Playing in front of their 100th consecutive sellout crowd, including the postseason, the Clippers trailed 90-83 with 8:20 remaining after Memphis opened the fourth quarter with a 9-2 run. They got as close as 90-88 on a 16-footer by Paul, but the Grizzlies extended their margin to 101-91 with an 11-3 run capped by Conley's jumper with 1:51 to play.
Randolph paced Memphis to a 52-51 halftime lead with 16 points and eight rebounds. The Clippers, who trailed 25-13 at the time of Allen's ejection, closed to 39-35 midway through the second period with a 9-2 spurt before reserve forward
Matt Barnes was scratched near his left eye by Randolph as the Grizzlies forward was being double-teamed by Barnes and Griffin down on the block.
Barnes was charged with a foul before going to the dressing room, and didn't report back in until 3:25 remained in the third quarter with the Clippers down 74-71. His two free throws put them ahead 78-76 with 1:14 left in the period, and the Grizzlies responded with a 19-footer by Randolph and a 3-pointer by Mike Miller before Clippers guard Darren Collison beat the buzzer with a 3-pointer of his own to tie it at 81.
The Grizzlies won the final four games of their first-round playoff semifinal series against the Clippers last spring after dropping the first two at Los Angeles, then got swept by San Antonio in the Western Conference finals. The previous season, the Clippers beat Memphis in seven games during the opening round, winning the deciding game on the road before getting swept by the Spurs in the conference semis.