Zetterlund scored with less than two and a half minutes left in regulation when he fired a shot past Capitals goaltender Logan Thompson.
His goal came less than two minutes after Washington's Alexei Protas tied the game 3–3.
David Perron, Ridley Greig and Nick Jensen also scored for Ottawa, while Leevi Merilainen stopped 26 shots to snap a three-game losing streak.
The Capitals (21-15-5), playing the back half of back-to-back games, took a 2-0 lead on goals from Tom Wilson and Dylan Strome. Washington goalie Logan Thompson made 28 saves.
After Merilainen stopped a series of shots from close range, Wilson grabbed the loose puck for his team-best 22nd of the season, giving the Capitals a 1-0 lead.
A little over a minute later, Protas awkwardly crashed into the boards after he and Artem Zub collided while racing for the puck. Protas was in no hurry to get up and left the game, but returned later.
The first-period spirit continued when Senators defenseman Thomas Chabot was taken down by Justin Sourdif. Drake Batherson dropped the gloves on Sourdif minutes later in the Senators forward's third career fight.
Strome made it 2-0 on a pass from Ryan Leonard and fired a long shot through traffic to beat a screened Merilainen.
Jensen cut the lead in half, scoring off a Jake Sanderson rebound at 7:42 of the second.
Late in the second period, Batherson scored a goal, but his shot went wide of the post. But Greig tied it with 28.8 seconds left in the frame when he deflected a shot that Thompson accidentally carried over the goal line.
Ottawa (19-15-5) then took the lead 2:47 into the third on Perron's goal.
Senators: Ottawa missed too many chances early in the game but managed to improve as the game went on.
Capitals: Washington started out strong, but the fact that they played back-to-back games in the back half showed late in the game.
Jake Sanderson recorded his 20th assist in 2025-26, becoming the first defenseman in Senators history to reach that mark in each of his first four seasons.
Stephen Holliday set up Perron, who one-timed Thompson to give the Senators their first lead of the game.
Senators: The Senators host the Winnipeg Jets on Saturday.
Capitals: Washington hosts the Chicago Blackhawks on Saturday.
