The Senators, trailing 2-0 in the Western Conference semifinal series, seemed destined to fall again, trailing 1-0 with less than a minute remaining in regulation and Pittsburgh on a power play.
Ottawa Coach Paul MacLean then pulled goalie Craig Anderson to add an attacker for a 5-on-5 situation, and the move paid off.
After a scoreless first overtime, Ottawa struck 7:39 into second extra frame when Andre Benoit launched a shot at Vokoun and Greening was there to backhand the rebound into the net.
Anderson turned aside 49-of-50 shots for the Sens, who took the longest game of the current post-season.
Tyler Kennedy scored and Vokoun ended with 46 stops of the Penguins, who will again attempt to put a stranglehold on the series in Wednesday's Game 4.