The Kings were rewarded for dominating in shots, scoring twice late in the third period to defeat the Canucks 3-2 at Rogers Arena on Thursday.
Los Angeles outshot Vancouver 40-16 and needed them all.
"We gritted it out and sometimes at the end of the game you look and say 'all right, that was justice' because I feel we dominated the game," said Williams. "We had the better opportunities and we were able to show some resiliency, some resolve and not give up."
Forward Dwight King started the comeback late in the second period and the Kings salvaged a three game Western Canadian trip by ending a five-game road losing streak. Los Angeles is 5-8-6 on the road, and Stoll hopes the comeback win can spark a turnaround in their play away from home.
"It was one of the best games we've played lately, especially on the road maybe this year and we needed that," Stoll said. "Hopefully we can use this as a little springboard for road games and get our road record going."
"One of the more disappointing games in a while. Just blew it at the end,” said goalie Ryan Miller, who made 37 saves.
Miller made a handful of great stops to keep the Canucks in the game before Williams power play wrist shot from just below the left faceoff dot beat him over the left shoulder on the short side.
"I've got to cover short side," said Miller. "It's my responsibility. It's frustrating to get to 57 minutes or so and blow it."
Williams' goal came on the Kings fourth power play and after failing to record a shot on the previous two opportunities against a Canucks penalty kill that had stopped 37 of the previous 39 chances.
"They scored a power play goal so we certainly have to answer," said Williams, who ended a seven-game goal drought. "There was a little bit of room and sometimes the shots go where you want."
Stoll put the Kings ahead with 1:14 left, taking a cross-ice pass from forward Tanner Pearson and slapping a bouncing puck past Miller's blocker to continue the Kings mastery of the Canucks. Los Angeles has won both meetings this season and six of the past seven.
"It was nice to get the two points and not give them any," Stoll said after scoring his first goal in 13 games. “It’s a good rivalry."
By winning in regulation Los Angeles moved one point ahead of Vancouver and into second place in the Pacific Division.
"I'm sure they’re frustrated," Kings coach Darryl Sutter said. "But that’s how the division is. It’s so close. It comes down to a big play, a bad goal or something almost every night."
The teams traded chances in the opening minutes, with Quick getting his right pad on two early shots in tight and Pearson hitting the post behind Miller from the slot.
Miller, who was pulled after allowing four goals on 22 shots in the first game against the Kings in November, got his glove on a chance from the slot by Anze Kopitar 7:30 into the game. Miller extended his right pad to stuff Los Angeles forward Tyler Toffoli alone in front of the net after a giveaway by Daniel Sedin and stopped King on a 2-on-1. The Kings had a 12-3 shot advantage, but the Canucks opened the scoring at 12:18 with captain Dustin Brown in the penalty box for tripping Jannik Hansen deep in the Vancouver end.
Vrbata shot the puck at the net from the top of the left faceoff circle and it bounced off Daniel Sedin’s skate, off Quick’s right pad and right to Burrows, who banged it between Quick's legs.
Los Angeles had a chance to tie the game on the power play early in the second period, but didn't manage a shot against the Canucks third-ranked penalty killing and Vrbata scored 11 seconds later.
"What we've done is shoot ourselves in the foot every game on this road trip being down 2-0," Williams said. "Battling back is tough in this League to get points and we got a big goal late to tie it up and then another one icing on the cake to get another point."
Vrbata's goal was Vancouver's only shot of the second period before the Kings, who hit the post on a power play seven minutes into the period, solved Miller with 5:21 left in it.
"We got out to a lead but we sat back all game," said Vancouver forward Brad Richardson, who played his 500th NHL game against his former team. "They pretty much had control of that game for the most part. In the end you still should have that win."
A short pass from Mike Richards left King alone cutting through the top of the crease. Miller reached out to stop his initial attempt with the paddle of his stick, but the rebound bounced back to King, who had time to lift it over the sprawled goalie.
Vancouver has been outshot 103-51 in its past three games and leaning heavily on Miller, who was making his fifth straight start for the second time this season.
"You can't expect to win when you get outshot 40 to something," Canucks captain Henrik Sedin said. "It's not good enough."