It lasted just 64 seconds before Zack Smith and the Senators retook the lead.
Bobby Ryan scored two goals and the Senators topped the Capitals 6-4.
"The big test for us was when they tied the game. We didn't handle momentum swings very well in the first period or in some previous games," said Ottawa coach Paul MacLean, whose team has dropped four of five coming in.
Smith scored the go-ahead goal with 2:23 remaining when he took a pass from Chris Neil at centre ice, skated in against defenceman Nate Schmidt and beat goaltender Braden Holtby from the left circle.
Smith's goal came after Washington's John Carlson tied the game with Smith in the penalty box.
Chris Phillips had a goal and an assist, and Mika Zibanejad and Colin Greening added goals for Ottawa. Erik Karlsson had two assists for the Senators, who trailed 3-1 after one period.
"Obviously a huge two points for us tonight," Phillips said. "We need to build off this momentum and keep it going. We look at the standings and we're not in a great spot right now. We need to get on a bit of a roll."
It was Ottawa's first win in regulation at the Verizon Center since March 12, 2006.
Eric Fehr, Marcus Johansson and Brooks Laich also scored for Washington, which led 3-1 before dropping its fourth straight.
"We played a solid game (losing Saturday) in Toronto; we played lousy tonight," Capitals coach Adam Oates said. "Not good decisions. We get a lead and we still don't do the right things."
Zibanejad had given Ottawa a 4-3 lead at 6:05 of the third when he deflected a Jason Spezza shot past Holtby for Ottawa's third power-play goal of the game.
Craig Anderson stopped 29 shots for Ottawa. Holtby made 35 saves for Washington.
Trailing 3-1 after one period, Ottawa tied it in the second as it outshot the Capitals 19-3.
"A lot of angry guys in here," Anderson said of the Ottawa locker room after the first 20 minutes.
"We weren't happy with our effort that first period. Obviously not happy with being down by two goals. But we held ourselves accountable. Each and every guy knew it wasn't good enough."
With a man advantage, Phillips skated down the left side and blasted a shot from the circle over Holtby's glove to make it 3-2 at 6:36 of the second period.
Exactly four minutes later, Greening tied it when he beat Holtby with a shot through traffic from the right circle.
"We had them," Carlson said. "We were close to putting our stamp on it. But we let them back."
After totalling three goals in its three previous games, Washington scored three in less than three minutes during the first period.
They broke a 1-1 tie with two goals 47 seconds apart.
During a power play, Alex Ovechkin's shot was deflected in front and Johansson banged the puck home at the 14:06 mark.
Washington made it 3-1 when Jason Chimera's pass deflected off Joel Ward's skate behind the end line out in front to Laich, who beat Anderson with a backhand for his fourth goal.
"We saw a very good hockey team in the first period with 18 shots and three goals and did a lot of things right," Laich said, "and for the rest of the game we saw a very bad hockey team. Bad decisions, bad penalties, getting outworked."
The Capitals took a 1-0 lead at 12:10 on a delayed penalty call when Fehr wristed a shot home from the slot.
Ottawa tied it on a power play just over a minute later as Ryan deflected Patrick Wiercioch's shot from the point for his 12th goal.
It was the first time this season the Capitals have allowed three power-play goals in a game, and the Washington penalty kill unit has given up at least one goal in the past six games.
NOTES: Capitals F Martin Erat, who on Monday demanded a trade, was a healthy scratch for the second straight game. ... Washington recalled D Tyson Strachan from Hershey of the AHL. Strachan fought Neil after Neil levelled Schmidt late in the first period. ... Ottawa's Mark Borowiecki (neck strain) was out of the lineup. The defenceman was rammed into the boards Sunday by Carolina F Kevin Westgarth, who received a two-game suspension for the hit.