Chandler Stephenson swept home a close-range rebound after defenceman Shea Theodore's powerful shot after just 1min 12sec of overtime to seal a dramatic come-from-behind victory for the Knights.
Dallas, beaten in overtime in game one on Friday, had looked poised to level the series after leading for most of regulation after goals from Miro Heiskanen and Jason Robertson.
But the T-Mobile Arena erupted with roars of relief and delight minutes before the end of the third quarter when Jonathan Marchessault tied it at 2-2 after a clever pass off the boards.
Vegas carried that momentum into overtime and Stephenson grabbed the winner to leave a shattered Stars team with little room for error if they are to haul themselves back into the series.
"First overtime goal in the playoffs, pretty cool," Stephenson said afterwards. "They had a good push and we didn't really have an answer, and we weren't really playing our best.
"There was emotion, frustration ... but playing here was deafening, and kind of gave us more energy," Stephenson said of the home crowd.
