Claude Giroux, Tim Stutzle and Thomas Chabot also scored, and Linus Ullmark made 16 saves for the Senators (13-6-2), who have points in five straight games (4-0-1).
Tommy Novak scored, and Sergei Murashov made 30 saves for the Penguins (7-11-2), who have lost six of their past eight games (2-5-1).
Egor Chinakhov nearly put Pittsburgh ahead on a breakaway at 3:07 of the first period, but his shot rang off the left post.
Novak seemed to give the Penguins a lead when he spun for a shot that went in off Senators defenseman Jordan Spence at 6:38. It was disallowed after the Senators challenged and the play was ruled offside.
Novak and Chinakhov then connected to put Pittsburgh in front 1-0 at 19:52. Chinakhov drove to the net for a backhand pass through the slot, setting up a wrist shot from Novak to the left of the crease for his team-leading eighth goal this season.
Amadio tied it 1-1 at 8:41 of the second period, intercepting a pass from Pittsburgh forward Connor Dewar and immediately scoring on a wrist shot from the slot.
Giroux gave Ottawa a 2-1 lead at 16:12. A backhand pass from Penguins forward Ben Kindel hit Amadio's skate and went to Giroux for a partial breakaway, allowing him to slip a backhand past Murashov's right pad.
Stutzle made it 3-1 at 14:18 of the third period, falling to his knees in the left face-off circle and whipping a wrist shot in off the inside of Murashov's left skate for his 11th goal of the season.
Chabot scored an empty-net goal at 19:28 for the 4-1 final.
