Haula took a pass from James Neal inside the blue line and then came in alone on the right side of the net, where he deked Kings goalie Jonathan Quick and fired a shot through his pads for his seventh career playoff goal.
The game was the longest ever played by a team in its inaugural season, and the longest in Kings franchise history.
Marc-Andre Fleury had 29 saves and Alex Tuch scored his first career playoff goal for Vegas. It was the 64th career playoff victory for Fleury, which moved him past Curtis Joseph into 12th place for all-time playoff wins.
Quick was brilliant, finishing with a career-high 54 saves for the Kings, who played without Norris Trophy contending defenseman Drew Doughty. Doughty was suspended for one game by the NHL's Department of Player Safety on Thursday for a Game 1 hit to the head of Vegas forward William Carrier, who did not play Friday.
Paul LaDue scored for Los Angeles, which fell to 29-28 all-time in Stanley Cup playoff overtime games.
The Golden Knights, who entered the contest 0-for-16 on the power play in their five games against the Kings, ended that streak in the first period with a little help from the dasher boards. With Kyle Clifford in the penalty box for goalie interference, Vegas took a 1-0 lead when Jonathan Marchessault's shot from the high slot caromed off the boards straight to Tuch, who easily slapped in the rebound past Quick's glove side.
It marked just the second power-play goal allowed in 13 games by Los Angeles, which led the NHL in penalty-kill percentage.
LaDue tied it with a power-play goal at the 15:55 mark of the second period with his first career playoff goal, firing a shot from the right point that glanced off the leg of Vegas defenseman Deryk Engelland in front of the net and past Fleury, ending a shutout streak of 95:55 by the Golden Knights' goalie.
The series now moves to the Staples Center in Los Angeles for the next two games, with Game 3 set for Sunday night.
--Field Level Media
Los Angeles | Vegas | |
Paul LaDue 1 | Points | Erik Haula 1 |
Paul LaDue 1 | Goals | Erik Haula 1 |
Michael Amadio 1 | Assists | Jonathan Marchessault 1 |
Paul LaDue 1 | Power Play Goals | Alex Tuch 1 |
N/A | Short Handed Goals | N/A |
Jonathan Quick .964 | Save Percentage | Marc-Andre Fleury .967 |
Jonathan Quick 54 | Saves | Marc-Andre Fleury 29 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Los Angeles | 30 | 1 | 1-3 | 3-4 | 8 | 51 |
Vegas | 56 | 2 | 1-4 | 2-3 | 6 | 42 |