Zetterlund, fresh off the bench, one-timed a cross-slot pass from Thomas Chabot past a sliding Logan Thompson.
Tim Stutzle had the secondary assist to extend his point streak to 11 games (18 points; eight goals, 10 assists).
David Perron, Ridly Greig and Nick Jensen scored, Shane Pinto had two assists, and Leevi Merilainen made 26 saves for the Senators (19-15-5), who trailed 2-0 after the first period.
Tom Wilson had a goal and an assist, and Dylan Strome and Aliaksei Protas scored for the Capitals (21-15-5), who have lost five of their past seven games (2-4-1). Thompson made 28 saves.
Wilson gave the Capitals a 1-0 lead at 8:13 of the first period. Merilainen made three saves in a span of three seconds before Wilson finished on a rebound. It was Wilson's fifth goal in three games.
Strome made it 2-0 with a power-play goal at 18:59. He skated in from the point and beat a screened Merilainen glove side with a wrist shot.
Jensen cut it to 2-1 at 7:42 of the second period. Moments after Jake Sanderson hit the cross bar, Jensen's shot from the right side beat Thompson before he could reset.
Greig tied it 2-2 at 19:31. He tipped a Pinto point shot, got his own rebound and the puck rattled around in the crease until Thompson accidentally kicked it in with his left leg.
Perron one-timed a centering pass from Stephen Halliday over Thompson's glove to give the Senators a 3-2 lead at 2:47 of the third period.
Protas took a centering feed from Justin Sourdif and beat Merilainen over the glove with a wrist shot from the middle of the slot to tie it 3-3 at 15:53.
