Williams rallied after missing shots in the closing minutes of regulation, when the Warriors ran off 11 straight points to force overtime tied at 106-all.
Montrezl Harrell added 23 points off the bench and rookie Shai Gilgeous-Alexander had 18.
The Clippers snapped a seven-game skid against the Warriors at Staples Center, where they last won on Dec. 25, 2014.
Kevin Durant had 33 points, 11 rebounds and 10 assists for the Warriors before fouling out with 3:46 left in the extra session. Klay Thompson added 31 points, but was just 5 of 16 on 3-pointers on a night without injured fellow Splash Brother Stephen Curry.
Golden State lost for just the third time in 14 games.
The starless Clippers improved to 6-1 at home.
Thompson's 3-pointer tied it 116-all in overtime, interrupting Williams' run of 10 straight points for the Clippers.
Down 106-95, the Warriors closed regulation on an 11-0 run, with Thompson scoring their last eight points. His second 3-pointer in the spurt tied it at 106.
The Clippers crashed the boards - every player grabbed at least one - and they dominated in the paint, 62-36.
Williams' 3-pointer gave Los Angeles its largest lead of 101-87. They didn't go up by double digits until Harrell's basket to open the fourth.
The Clippers shot 60 percent and led 64-61 at halftime. They controlled the boards, 23-13, and owned a 30-18 edge in the paint.
Durant scored 21 points and had three fouls in the half for the Warriors.
Warriors: They fell to 39-60 in regular-season games without Curry (left groin strain), who missed his second straight game. ... F Draymond Green returned to the lineup after sitting out two games with a right foot-toe sprain. ... G Shaun Livingston was back after being out seven games with right foot soreness. ... They haven't left California during a seven-game stretch that concludes Tuesday.
Clippers: Hall of Famer Bill Russell sat courtside with owner Steve Ballmer.
Warriors: Host Atlanta on Tuesday in the second game of a back-to-back, their third of the season.
Clippers: Host San Antonio on Thursday, their second straight division-leading opponent.
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