Williams scored 16 points and keyed a fourth-quarter rally and the Clippers snapped Memphis' four-game winning streak with an 82-81 victory over the Grizzlies on Tuesday night.
Williams had nine points in the final period, including six straight points in the closing 1:49.
"We just battled," Clippers coach Vinny del Negro said. "It wasn't perfect, but we made enough plays. We threw the ball away enough [20 turnovers], especially on the break, but we found a way. Mo hit that big 3 out of a timeout that we designed. Like I said, it comes down to execution."
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Blake Griffin added 15 points and 14 rebounds for the Clippers, while Chris Kaman finished with 14 points. Eric Gordon scored 11 points.
Mike Conley scored 20 points to lead the Grizzlies, while Zach Randolph and Marc Gasol had 14 points apiece, Gasol added 15 rebounds. Sam Young scored 13 points for Memphis, which remained in the Western Conference's eighth and final playoff spot.
Los Angeles was able to overcome a 13-point Memphis lead in the third quarter with a rally to open the fourth period.
The Clippers outscored the Grizzlies 23-13 in the final period, the lowest fourth quarter output of the season for Memphis.
"[The Clippers] did a good job of defending us," Memphis coach Lionel Hollins said. "It was a dogfight. It was one of those games where it was just going to be that way. It looked like we felt like we could turn it on anytime, and we had spurts where we did.
Memphis was still able to hold onto the eighth playoff spot in the Western Conference.
The Houston Rockets, who are in the ninth spot just outside the playoffs, lost 104-101 to the Sacramento Kings, dropping Memphis' magic number to two for a playoff berth.
Memphis is a half game behind the New Orleans Hornets, who were idle Tuesday night, for the seventh seed.
"It was a tough game all around," Randolph said. "I don't think we came out ready. [We] came out taking this team too lightly. Let them stick around in the game. And you see what happened."
The game's closing seconds were marked with confusion and a review by officials.
With 5.7 seconds left, Clippers guard 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 differed on 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.
"I had no idea," Griffin said when asked if he understood what happened on the play. "I was talking to one ref, and he called a charge. [Official] Violet [Palmer] called a block. Then I heard them talking about the time and talking about the shot clock."
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.
"You can't take these teams lightly, these teams that don't have nothing to do for the postseason," Allen said. "They're coming out here and playing with pride."
The Grizzlies closed the third 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.
"Our bench did a great job of getting us back at the start of the fourth quarter," Williams said.
Greivis Vasquez finally ended the Memphis slump with a 3-pointer, then Allen broke free for a dunk.
The teams then exchanged 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.
Griffin said the Clippers approach is not to look so much at a spoiler's role as it is to continue to improve.
"It's not a mindset of 'Oh we don't want them to get to the playoffs,' or anything like that," he said. "For us, it's about finishing the year out. It's just pride this time of the year. We want to do the best and play as well together as possible."
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. Griffin's double-double was his 60th of the season. Memphis had won six straight home games before the loss, and it was the first time the Grizzlies had dropped a home game to a sub-.500 team since losing to the New Jersey Nets on Dec. 21.