Alex Ovechkin netted the game-winner with 51 2, at Verizon Center.
Keith Aucoin and Marcus Johansson scored in regulation for Washington, which snapped a three-game slide to end a five-game homestand with a 2-2-1 record. Tomas Vokoun made 24 saves in the win.
Ryan Malone and Teddy Purcell tallied goals for the Lightning, who lost their second consecutive contest on the heels of a four-game win streak.
Dustin Tokarski made his first career start for Tampa Bay and stopped 29-of-32 shots in defeat.
"I thought he was great. He was excellent. He battled," Lightning defenseman Mike Commodore said about Tokarski. "The puck hit him and there were no rebounds."
The Capitals trailed 2-1 entering the third period, but were able to net the equalizer with 4:58 remaining in regulation when Dennis Wideman slapped the puck out of a scrum on the right boards to a wide open Johansson in the slot and he finished with a wrister through the pads of Tokarski.
"We just had to get the puck in deep and work," Capitals head coach Dale Hunter said. "It creates scoring chances."
Vokoun faced just three shots in the third period to force the extra frame.
Then, as time was winding down in OT, Jason Chimera fought off a defender in the left corner before feeding a pass to Dmitry Orlov in the slot, where he faked a shot before moving the puck along to Ovechkin to the right of the net and he one-timed it into the short side for the game-deciding goal.
Washington carried a 1-0 lead into the second period after Karl Alzner's slap shot from the left point, which would have gone wide to the left, was deflected into the net with the shaft of Aucoin's stick with 2:52 left in the opening period.
But Malone knotted the game at one at the 7:25 mark of the second period after the Lightning were awarded a power play because of a Wideman boarding penalty. Tampa Bay took advantage of the extra attacker less than 30 seconds into the power play when Steven Stamkos threw the puck towards the slot from the right corner that deflected into the net off the skate of Malone.
The play was reviewed but the goal was upheld as Malone made no kicking motion with his skate.
The Lightning used another man advantage to take a 2-1 lead with 1:18 left in the middle stanza when Purcell's wrister from the left circle was kicked aside by Vokoun, but the rebound bounced off the tip of Capitals defenseman John Carlson's skate and skipped across the goal line.
Washington leads the season series 3-2, with the home team winning every game...The Capitals improved to 22-10-3 at home this season, while the Lightning fell to 11-19-5 on the road...Tokarski had appeared in two games in relief for Tampa Bay during the 2009-10 season...Washington went 0-for-2 on the power play...Tampa Bay was 2-for-3 with the man advantage.