Despite being outplayed for much of the game — as evident by the shot disparity of 28-13 through two periods — the Penguins entered the third in a 2-2 tie.
Pittsburgh overcame a pair of New York power plays in the second — including one for too many men on the ice that had coach Dan Bylsma irate on the bench — and got even again when Dupuis scored his fifth of the series with 9:01 remaining.
Joe Vitale raced along the right wing boards and flung the puck in front to Dupuis, who redirected it past Nabokov.
Pittsburgh nearly took its first lead of the night in the final minute of the second when Crosby eluded Frans Nielsen behind the New York net and found Chris Kunitz at the right post for a quick one-timer that Nabokov blocked.
The Islanders showed no signs of nervousness or that the moment was too big for them, despite the lack of playoff experience throughout the roster.
New York forced the Penguins into an early icing violation that caused Bylsma to burn his lone timeout just 1:19 in in order to rest the tired players forced to stay on the ice.
The Islanders kept the pressure on, and spent a large chunk of time in the Pittsburgh end — largely in the corners and behind the net — but it paid off with an early goal.
Josh Bailey dug the puck out of the right corner and fed a perfect backhanded pass out to Tavares, who was left alone as he skated into the slot. Tavares grabbed the puck and snapped off a crisp wrist shot from the hashmarks that beat Vokoun at 5:36.
As the Islanders celebrated, Tavares was showered with chants of "M-V-P, M-V-P" one day after he was announced as a finalist for the Hart Trophy.
The goal carried even more significance than the 1-0 lead it created as it was the Islanders' first against Vokoun in two games this series.
Counting the regular season and his shutout win Thursday in Game 5, Vokoun entered with a 4-0 mark, an 0.69 goals-against average, and .977 save percentage this year in five games against the Islanders.
But Crosby, also one of the three Hart finalists, created the tying goal with a strong, unimpeded drive on Nabokov. Crosby surged to the net and put a backhand on the goal. Nabokov made the stop, but couldn't grab the puck before Iginla came into the middle and poked the rebound in at 7:39.
It appeared the game would remain tied until the intermission, however McDonald put the Islanders back in front 2-1 with 37 seconds left in the first.
More hard work on the end boards led to the goal as Grabner fought off Martin and managed to shove the puck out front to Aucoin, who quickly sent a pass across the crease from the left post to the right, where McDonald was left unchecked. In one motion he steered the puck into the open side before Vokoun could recover.
NOTES: This was the 16th overtime game of the first round, tying last year's record. Home teams are 10-6 after going 4-12 in 2012. ... Dupuis had five goals and two assists in the series, earning at least one point in all six games. ... C Brock Nelson made his NHL debut for the Islanders. LW Jesse Joensuu, who played in Game 5, sat out. ... Malkin had nine assists in the series.