The Stars cut the deficit in the best-of-seven Western Conference final to 3-1, forcing a game five in Las Vegas on Saturday as the teams vie to face the Eastern Conference champion Florida Panthers in the Stanley Cup Final.
Left wing Jason Robertson scored twice for the Stars, who played without suspended captain Jamie Benn.
Benn was suspended for two games by the NHL for a cross-check near the neck of Vegas captain Mark Stone -- as Stone lay on the ice early in game three on Tuesday.
Dallas goalie Jake Oettinger had 37 saves, two nights after he was yanked in the first period of game three.
Center William Karlsson and right wing Jonathan Marchessault scored for the Knights.
The winners of the series will face the Florida Panthers, who swept the Carolina Hurricanes in the Eastern Conference final.
Pavelski grabbed the game-winner at 3:18 of overtime, firing a one-timer from the left face-off circle after Vegas defenceman Brayden McNabb was penalized for high-sticking.
The Golden Knights took a 1-0 lead at 4:17 of the first when Karlsson tipped in Reilly Smith's shot from inside the right circle.
Robertson tied it 1-1 on a power play at 15:42, but Marchessault gave Vegas a 2-1 lead at 10:23 of the second period after McNabb sent a pass across the crease and between the legs of Stars defenceman Ryan Suter.
Robertson knotted the score at 2-2 at 17:21 of the second with a backhand off a deflection.
