Williams had nine points in the final period, including six straight points in the final 1:49 to give Los Angeles enough of a buffer for the victory, despite a wild ending that saw the Clippers run off the clock after a jump ball with 5.7 seconds left.
Neither team shot well with the Clippers at 41 percent, while Memphis was at 40 percent.
Despite the loss, Memphis was still able to hold onto the eighth playoff spot in the Western Conference.
Memphis is a half game behind the New Orleans Hornets, who were idle Tuesday night, for the seventh seed.
The game's closing seconds were marked with confusion and a review by officials.
With 5.7 seconds left, Eric Bledsoe stumbled out of control down the lane, running into Tony Allen. Officials reviewed the play to see if there was a shot clock violation.
They ruled there was no shot clock violation, but officials couldn't decide whether to call Allen for a block or Bledsoe for a charge. A double foul was the result, leading to a jump ball.
The Clippers controlled the tip and ran out the clock, as the Grizzlies couldn't reach them to foul.
Memphis, which led by 11 in the first half, carried a 43-39 lead into the break, but allowed Los Angeles to close with five straight points, including Gordon's runner in the lane as time expired in the half.
Kaman had 10 points for the Clippers. Griffin, who was held to a season-low eight points in the March 14 game against the Grizzlies, was 3 of 9 in the half for six points.
No Memphis player was in double figures.
The first half was dominated by inaccurate shooting as Memphis was 39 percent from the field, compared to 42 percent for the Clippers, who added 10 turnovers.
The Clippers made runs at the Memphis lead after halftime, cutting it to four points at times. The shooting didn't improve much for either side, but Memphis was able to stretch it to 13 near the midway point of the third.
Los Angeles still stayed relatively close, and late in the quarter again cut the Memphis lead to four at 63-59.
The Grizzlies closed the quarter with a small rally to carry a 68-59 lead into the fourth.
The Clippers weren't through, however, opening the fourth quarter with 10 straight points, including a pair of jumpers from Kaman. That erased the Memphis lead and put Los Angeles up 69-68 as the Grizzlies missed their first six shots of the period.
Greivis Vasquez finally ended the Memphis slump with a 3-pointer, then Allen broke free for a dunk.
The teams then exchanged leads before Allen's defense and hustle helped Memphis maintain the lead until the 2-minute mark. A 3-pointer by Williams with 1:49 left, followed by a 3-point play from the Clippers guard, put Los Angeles up 82-79 with 1:31 to play.
Conley's layup with 29.5 seconds left cut the lead to 82-81 before the final confusing seconds.
NOTES: The Grizzlies announced earlier Tuesday that first-round playoff tickets will go on sale Sunday. ... Griffin's eight points in the March 14 loss to the Grizzlies was not only his lowest point total of the season, but the only time he didn't reach double figures. ... Memphis had won all 21 home games in which it was ahead at halftime before Tuesday's loss.