Only the final lead was safe in Game 4.
Tavares slammed in his own rebound in front after Brad Boyes fed him following a turnover by Penguins star Evgeni Malkin. It was the Islanders' third one-goal advantage in the game and the one that earned them a 2-2 tie in the highly entertaining series that has featured 5-4 and 6-4 finishes at Nassau Coliseum.
Tavares was serenaded with cheers of "M-V-P" from the frantic crowd that is believing an upset is possible. Casey Cizikas shoved in a shot with 1:16 left to add some much-needed insurance.
Captain Mark Streit scored twice, and Brian Strait and Kyle Okposo also had goals. Evgeni Nabokov made 27 saves for the eighth-seeded Islanders, who know they will last at least six games with the top-seeded Penguins.
Game 5 is Thursday in Pittsburgh.