Mike Hoffman, Marc Methot, Derick Brassard, Zack Smith and Kyle Turris scored for the Senators, who now lead the best-of-seven series 2-1.
Sidney Crosby replied for the Penguins, who trailed 5-0 after two periods.
The Senators chased Penguins starting goalie Marc-Andre Fleury with four goals on nine shots in the first 12:52. Fleury was replaced by Matt Murray, who made 19 saves.
Craig Anderson made 25 shots in the Senators net. He lost his bid for a shutout when Crosby deflected a Phil Kessel shot though his legs at 6:07 of the third.
Hoffman opened the scoring at the 48-second mark, banking a shot in off Fleury from behind the goal line for his fifth goal of the playoffs.
Methot made it 2-0 at 10:34, taking a short pass from Bobby Ryan at the side of the net, then banging home his own rebound after his initial shot was stopped.
Brassard converted a setup by Clarke MacArthur into an open side at 12:28, and Smith chased Fleury 24 seconds later when he grabbed the puck behind the net and slid home a backhand on the wraparound.
Turris made it 5-0 when he scored on the 12th shot against Murray at 18:18 of the second period, grabbing the puck after Hoffman's attempt was blocked and cutting across the front to backhand home his fourth of the playoffs.
NOTES: The Senators set a franchise playoff record by scoring three times in a span of 2:18. ... Senators D Marc Methot scored for the second time in eight games after going goalless for more than a year. ... The Penguins went with seven defensemen, adding veterans Trevor Daley and Mark Streit with Justin Schultz out. Daley was injured in Game 5 of the second-round series against Washington. Streit appeared in his first game of the playoffs. ... Schultz, injured RW Bryan Rust and injured RW Patric Hornqvist all skated Wednesday morning.