Fisher, selected the NHL's third star of the week earlier in the day, batted Chris Phillips' centering pass out of the air and past Semyon Varlamov for his 10th goal of the season.
The Senators won their fourth in a row to take the division lead with 27 points, one ahead of the idle Sabres and Boston, which gained a share of second place with a 4-2 win in St. Louis.
"We've been elevating our game against top teams and that's a great sign," Fisher said.
Brian Elliott made 25 saves in his fifth start for the Senators, who rallied from a 3-1 deficit in the third period to win their fourth in a row and wrap up a 4-0-1 homestand.
Alexandre Picard scored Ottawa's second goal in a span of 4:20 on a power play 7:40 into the third to tie it at 3. Filip Kuba had three assists, setting up each of the Senators' last three goals.
"We made some adjustments in the neutral zone," Fisher said. "We did a few different things coming into the third and we started moving our feet a little bit more and drew some penalties. We were hungry and we knew that we could come back."
Peter Regin gave the Senators a 1-0 lead 7:27 in before Ottawa allowed three straight goals.
Chris Neil got his fourth goal 3:18 into the third to draw the Senators to 3-2 before Picard beat Varlamov with a slap shot from the point to tie it after Alex Ovechkin was called for roughing at 6:43.
"You score to win," Beagle said. "It's a tough loss. I still can't really believe that we let it slip away. I scored but at the same point you're disappointed with the loss so it's kind of a bitter feeling."
Varlamov stopped 33 shots for the injury-ravaged Capitals, who have dropped four of five (1-2-2), including a 2-1 shootout loss Saturday in Toronto.
"This was a collapse by 20 guys and I don't know how else to sugarcoat it," Washington coach Bruce Boudreau said. "We had total control of the game after two. They didn't even want to be part of the game -- it looked like they wanted to go home. Something lit a fire under them and we couldn't match it."
The Capitals, who sit atop the Southeast Division with 32 points, dropped into a tie for the conference lead with Pittsburgh, which beat Florida 3-2 in overtime.
Regin opened the scoring off a deflection. He tipped Jesse Winchester's shot past Varlamov from the edge of the crease for his third goal.
Clark drew Washington even at 11:19 when Brian Pothier's slap pass went in off the Washington captain's left skate. Ovechkin drew an assist for his pass to Pothier to begin the play -- and the goal was upheld by a video review.
Morrison gave Washington the lead with 29.3 seconds left in the first when he skated past the crease to redirect Mike Green's pass for his eighth goal.
Beagle made it a 3-1 advantage with an unassisted effort 11:44 into the second. The 24-year-old rookie beat Elliott with a snap shot from the slot after the puck landed at his feet when Senators forward Jonathan Cheechoo's backhand clearing attempt struck him on the skate.
"You can't ask for a better opportunity," Beagle said.
Elliott stopped 14 shots in the third period of Saturday's 5-3 win over Buffalo after taking over for Pascal Leclaire, who left after the second with a lower-body injury. ... Capitals C David Steckel scooped up the puck from Beagle's goal and flipped it to the Capitals' bench. Ovechkin congratulated Beagle moments later, skating up to the boards to knock helmets with him as he sat on the bench. ... Beagle recorded his first career point with an assist in his season debut, a 4-2 road win over the New York Rangers on Tuesday. He had no points in three games with Washington last season. ... Leclaire was in uniform as Elliott's backup. ... Fisher had two goals and four assists in three games last week.
Copyright by STATS LLC and The Associated Press
Arena: Canadian Tire Centre Location: Ottawa, Ontario
Referees: Marc Joannette, Bill McCreary Linesmen: Michel Cormier, Greg Devorski
Attendance: 16,210 (87.6% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Peter Regin (3)
Assists: Jesse Winchester, Ryan Shannon
Chris Clark (2)
Assists: Brian Pothier, Alex Ovechkin
Brendan Morrison (8)
Assists: Mike Green, Eric Fehr
Jay Beagle (1)
Chris Neil (4)
Assist: Filip Kuba
Alexandre Picard (2)
(Power Play) Assists: Filip Kuba, Milan Michalek
Mike Fisher (10)
Assists: Chris Phillips, Filip Kuba