Evgeny Kuznetsov and Lars Eller each had a goal and two assists, Ovechkin and Tom Wilson each had a goal and an assist, and Braden Holtby made 33 saves for Washington, which is 7-1 on the road in the Stanley Cup Playoffs, tying its record for most road wins in one postseason.
Brayden Point and Steven Stamkos scored, and Andrei Vasilevskiy made 31 saves for Tampa Bay, which lost two games in a row for the first time this postseason.
"If there is one thing I can sit here and say about these two games, it's we just played tentative and a little bit slow," Lightning coach Jon Cooper said. "We didn't get 113 points by playing that way. We didn't win the first two rounds by playing that way. These first two games, that's the way we've played."
Washington's Devante Smith-Pelly tied it 2-2 at 2:50 of the second period on a one-timer off a pass from Alex Chiasson on a 2-on-1.
"That was a big, big goal for our group, and after that, I think it really changed," Capitals forward Brett Connolly said. "Everything changed, and we just kept pushing and pushing, and then we got it to 6-2."
Eller gave Washington a 3-2 lead at 18:58, scoring from in front on a redirection of Jakub Vrana's pass out of the right corner.
Kuznetsov made it 4-2 with a power-play goal at 19:57, less than seven seconds after Vasilevskiy was called for a tripping penalty. He sent a pass along the right goal line through the crease, where it deflected off Lightning defenseman Ryan McDonagh's stick into the net.
It's the second straight game the Capitals scored a power-play goal late in a period to take a two-goal lead (Ovechkin scored at 19:54 of the first period in Game 1 to give Washington a 2-0 lead).
"You'd think we'd learn from our mistake in Game 1, but they get one and that's really a killer going down 4-2 instead of 3-2," Stamkos said. "It's little details of the game at this time of the year, and they've executed and we haven't."
Ovechkin extended the lead to 5-2 at 3:34 of the third period on a one-timer off a pass from Kuznetsov. Connolly made it 6-2 at 12:57, beating Vasilevskiy blocker side from the top of the left circle.
"I said it this morning, everyone is stepping up," Ovechkin said. "We played hard. We played smart and you can see all the four lines did their job. We didn't force it. We just did our job."
Wilson gave the Capitals a 1-0 lead 28 seconds into the game, redirecting Matt Niskanen's shot from the right point.
Point tied it 1-1 at 7:08 with a power-play goal. Stamkos gave the Lightning a 2-1 lead on a one-timer on the power play at 10:22.
