In his first start of the season in place of 92.
Irving suffered the concussion after being kneed in the head during the fourth quarter of Tuesday's loss to the Miami Heat. He experienced headaches after the game that worsened over the course of the night and during pregame activities prior to Wednesday's contest.
"Obviously you could feel sorry for yourself and say one of our best players is out and go in the tank, or you could respond like we did," said Cleveland head coach Byron Scott.
Los Angeles' Caron Butler had a chance to tie the game at 95 with 9.8 seconds left, but his three-pointer from the left wing was off the mark.
Antawn Jamison finished with 27 points and eight rebounds for Cleveland, which won for the second time in three games.
Paul finished with 16 points and 12 assists, while Blake Griffin had 25 points and 15 boards for the Clippers, who had won six of their last seven games coming in. Randy Foye started in place of the injured Chauncey Billups, who is out for the season after suffering a torn left Achilles in Monday's game, and netted 15 points.
"We came out flat, I couldn't make a shot, we didn't defend well" said Paul, who finished 5-of-16 from the floor.
Kenyon Martin made his season debut for the Clippers and scored six points. Martin played for the Xinjiang Tigers of the Chinese Basketball Association during the NBA lockout, and was contractually obligated to wait until the end of the Tigers' season before returning to the NBA. He was cleared to play by FIBA, basketball's international governing body last week.
Down by as many as 15 points in the second half, two Paul free throws knotted the game at 87 with 2:10 left in the fourth. But Daniel Gibson's trey and a pair of Session free throws pushed the lead back to five with 56.7 seconds left.
Griffin's three-point play cut the deficit back to two, 94-92, with 17.3 seconds remaining and Gibson gave the Clippers life after making 1-of-2 from the line to keep it a one-possession contest with 16.4 to go.
But Butler missed a trey at the other end and Alonzo Gee and Gibson went a perfect 4-for-4 from the charity stripe in the closing seconds to seal the win.
Foye netted eight points while Paul dished out six assists as the Clippers took a 24-19 lead into the second quarter.
A 7-0 spurt by the Cavs, capped by Christian Eyenga's trey and driving layup, gave Cleveland its first advantage of the contest, 29-28, with 5:01 left in the second. The contest was knotted at 40 heading into the break.
The Cavs began the second half on a 17-4 surge, giving the hosts a 57-44 advantage midway through the third stanza. Cleveland led by as many as 15 in the quarter before taking a 70-64 advantage going into the fourth.
Cleveland is 9-0 when leading after three quarters...The Clippers have lost 10 consecutive games to the Cavaliers in Cleveland...Los Angeles' Butler scored 21 points...Anderson Varejao had 15 points and 11 rebounds for Cleveland.