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Joel Kiviranta also scored a powerplay goal late in the third period goal to force overtime as the Stars rallied from a 2-0 deficit Monday night to shock the Golden Knights and win the Western Conference final series 4-1.
"We found our game. We scored a goal and that got us going, then the powerplay took over," said forward Joe Pavelski of the Stars' eighth come-from-behind win in the post season.
On the winning goal, Gurianov, 23, took a pass from John Klingberg and hammered a one-timer past Vegas goalie Robin Lehner on the short side that sparked a mob scene celebration with Dallas goalie Anton Khudobin in the middle.
Canada's Jamie Benn also scored while Khudobin stopped 34 shots for the Stars, who advanced to their first Stanley Cup final since 2000.
The Lightning can wrap their series up with a win on Tuesday in the NHL's quarantine bubble in Edmonton, Alberta.
Dallas has been outshot and outplayed for most of the series, but thanks to timely scoring and brilliant goaltending from Russia's Khudobin they were able to stun the favoured Golden Knights.
Khudobin, who stopped 153 of 161 shots in the series, assumed the starting role last month from Ben Bishop, who is injured.
"He stepped into an unsure situation and just ran with it. He got more confident with every game," Pavelski said of Khudobin.
Vegas coach Pete DeBoer said his teams scoring woes started in the previous round against the Vancouver Canucks and carried over into the conference final.
"There's no doubt the last couple games of the Vancouver series against (Canucks goalie Thatcher) Demko probably rattled our confidence in that area as a group," DeBoer said. "Honestly up to that point, I thought we were creating a ton of offence."
Stephenson took a cross-ice pass from Theodore and drove to the net where he neatly slipped a backhand between the legs of Khudobin.
Smith broke out quickly, creating a two-on-one and then ripped a shot on the short side over the glove of Khudobin.
Benn cut the deficit to 2-1 by outbattling defenceman Alec Martinez for a loose puck and then turning and firing it high into the net.
Kiviranta tied it up on the powerplay, lifting the puck over a sprawled Lehner during a goal mouth scramble with 3:47 left in the regulation.