Viktor Kozlov had two goals and Alexander Ovechkin three assists for the Capitals, who host the decider for the best-of-seven series decider on Wednesday.
Pittsburgh's Sidney Crosby sent the game into overtime with his 10th goal of the postseason, a backhander with 4:18 remaining in regulation.
The Penguins' Bill Guerin had the only goal of the first period off an assist by Crosby.
The teams were level at 2-2 after the second when Kozlov and Tomas Fleischmann scored for Washington and Mark Eaton added a power play goal for Pittsburgh.
A busy third period saw two goals by each team.
Kris Letang scored on a power play for the Penguins before Alexander Semin and Kozlov tallied for the Capitals, Semin scoring on a power play.
Crosby closed out the regulation scoring off Evgeni Malkin's third assist of the game.
