Brooks Laich and Jason Chimera also scored for the Capitals, who moved within three points of the first-place Lightning. Washington had gone 0-1-2 in its previous three games, scoring just three goals over that stretch.
Tampa Bay, which had a six-game winning streak snapped, got goals from Teddy Purcell and Brett Clark.
The game occasionally saw Washington keep the puck in its end of the ice until Tampa Bay, which lined up in an 1-3-1 defensive setup in the neutral zone, sent a forechecker in from center ice.
After Laich scored at 6:38 of the second, Ovechkin made it 3-1 on a power-play goal 1:47 later. It was Ovechkin's 20th goal this season, coming in his 53rd game.
Clark cut the deficit to 3-2 during a power play with 40.1 seconds left in the second. It stopped a personal 19-game goal drought.
The Capitals went ahead 4-2 on Backstrom's second of the game at 12:22 of the third. Chimera had an empty-net goal with 37.1 seconds remaining.
Washington got the game's first six shots, however, the Capitals fell behind 1-0 when Purcell scored on Tampa Bay's initial shot at 3:21 of the first.
The Capitals then got the next six shots after Purcell's goal, with Backstrom tying it at 1 against Dwayne Roloson on Washington's 12th shot 9:09 into the game.
Roloson entered with two consecutive shutout wins over Washington, and shutouts in his previous two games overall. Backstrom's goal was the Capitals' first against Tampa Bay in 139 minutes, 22 seconds.
The opening period featured 23 shots (17 by Washington), a pair of fights and a scrum in the crease that saw Roloson get a roughing penalty for jabbing Washington's Matt Hendricks - who was given a goaltender interference penalty - several times with his glove.
Notes: Purcell also had an assist, giving him four goals and nine points over his last four games. ... Washington LW Alexander Semin (groin) has resumed practicing, but missed his 11th straight game. ... Tampa Bay LW Ryan Malone (mid-body) sat out his fourth consecutive game. ... Ovechkin stopped to play floor hockey on a mini-rink with a group of kids just outside the locker room area after arriving for the game.