Ryan Smyth set up the game-winning tally for the Kings, who beat the visitors on home ice for the first time since November 6, 1997 at the Great Western Forum.
Quick improved to 8-1-0 on the season with his ninth career shutout for the hosts, who have won their initial five home games for the first time since 1980-81.
"It's a team effort. You just look at the way we played tonight, it's one of the top offenses in the league and they didn't get too many quality scoring chances," Quick said. "We were extremely responsible in the defensive zone and we were smart and didn't take too many penalties."
Mike Smith was the hard-luck loser, turning away 25 shots in defeat for the Lightning, who have dropped two in a row following wins in three out of four.
Anze Kopitar was denied by a sprawling Smith on a short-handed breakaway with about nine minutes left in the second period to keep the game scoreless.
LA finally broke through with 14:40 to play in the game
Mathieu Roy's attempted outlet pass hit Dana Tyrell's skate and was picked up by Smyth just inside the Bolts blueline. Smith backhanded a pass that Williams received on his backhand with his back to the net. Williams then spun to his forehand and slipped a shot past Smith to match a career-best with a goal in four straight games.
"They got an extra break at the end there in the third and got a goal but it was a hard fought game by both teams," Smith said. "Just because they beat us doesn't mean we're a bad hockey team. Tonight wasn't our night, but I think we'll be better because of this game."
Tampa Bay pulled Smith with 50 seconds to play for the extra attacker but could not muster a good scoring chance over the next 20 seconds before the Kings cleared the zone.
The Lightning got the puck back in the attack zone for Martin St. Louis, who was denied on a wrister from the bottom of the right circle with 16 ticks to go. Tampa Bay sent a couple of shots toward the next in the final seconds but could not dent Quick.
The Kings were 0-5-2 against the Lightning at Staples Center before Thursday. Williams also tallied in four straight contests from December 19-26, 2006...He has scored 11 points in his last 10 games while Smyth has totaled eight points in his last 10 matches...Jarret Stoll, the third member of that line, picked up an assist and now has 11 points in his last 10 games...Quick is tied with Mario Lessard for the sixth most shutouts in team history...LA defenseman Drew Doughty returned to the lineup after missing the last six games because of a concussion...The Kings are off to their second best 12-game start in franchise history with 18 points...The best 12-game start came in 1980-81 when they went 10-1-1 for 21 points...Smith suffered his first loss in six starts against the Kings...The Lightning are 4-2-1 on the road.