T.J. Oshie scored two goals and Devante Smith-Pelly had one, and Braden Holtby made 24 saves for the Capitals, who won at home for the first time in the series. They are 4-5 at home in the Stanley Cup Playoffs and 7-2 on the road.
It was Holtby's first shutout of the season, regular season included, and the fifth of his NHL playoff career.
"It's a perfect time," Smith-Pelly said of Holtby's first shutout since April 5, 2017. "He's been great all year. Obviously an up-and-down year for him personally, but the way he's bounced back, he's been amazing all throughout the playoffs, and really, really happy for him."
Andrei Vasilevskiy made 31 saves for the Lightning, who won the three previous games, including Games 3 and 4 here. They are 5-2 on the road in the playoffs and 6-3 at home.
Tampa Bay was shut out for the first time this postseason after scoring at least two goals in its first 15 games, including three or more in 11.
The Lightning haven't scored since Ryan Callahan's goal 33 seconds into the second period of Game 5, a drought of 99:27.
The Capitals outshot the Lightning 34-24 and outhit them 39-19. It was Washington's most physical game of the series.
"We were no good," Tampa Bay coach Jon Cooper said. "We didn't play with near the desperation they did. Was it a fairly even game? There's no question. But what were the hits, 39-19? Somebody was engaged and somebody wasn't. That's a choice."
Oshie gave the Capitals a 1-0 lead with a power-play goal off a one-timer from above the right hash marks at 15:12 of the second period. Backstrom threaded the pass to Oshie from the right face-off circle.
It was Washington's first power play since 7:08 of the second period in Game 4.
"I think the biggest thing there is No. 8 [Alex Ovechkin] in his office over there," said Oshie, who ended a six-game goal drought with his sixth of the playoffs. "Everything, how teams play us, all depends on where he is and how they want to play him. For me, it's just a matter of a couple feet here and there to try and find a soft area. Whether it's Nick or [Evgeny Kuznetsov], they're able to get the puck into the wheelhouse, and it's up to me to find a hole."
Smith-Pelly made it 2-0 at 10:02 of the third period, scoring on a one-timer from the right hash marks off a pass from behind the net from Chandler Stephenson. It was Smith-Pelly's fourth goal of the playoffs and second of the series. He also scored in Game 2.
Oshie scored an empty-net goal at 19:10 of the third period to make it 3-0.
"They played like it was the last game," Lightning captain Steven Stamkos said. "We played like it might be our last game. The desperation needs to be higher, and I expect it to be."
