The Lightning (8-3-1) have won three straight games on their four-game homestand. They will host the Calgary Flames on Thursday.
Garrison's second goal of the season came after center Steven Stamkos won a faceoff in the offensive zone, and the defenseman sent a slap shot between several players past Capitals goalie Braden Holtby.
"We were pretty loose on defense tonight, probably as loose as we've been all season," Lightning coach Jon Cooper said. "We needed some big saves and we did the most with our chances on offense."
The Capitals took a 2-1 lead 2:11 into the second period after some strong goaltending by Holtby set up opportunities on offense. After a save on a one-timer by Lightning wing Ondrej Palat, the Capitals went on transition and Eric Fehr scored on a rebound of his missed shot. The sharp-angle wrist shot went above goalie Ben Bishop's shoulder and to the top of the net.
"I let three in tonight and that was enough," Bishop said. "It was probably more than enough to be honest because I wanted to shut the door. But we know this was going to be a tough game and now we've got three in a row on this homestand. We'll rest up over the next couple of days and get back to work."
The Lightning answered with two goals to take a 3-2 lead. Palat tied the game at 9:29 in the second period when he took a feed from Nikita Kucherov and sent a one-timer past Holtby. Kucherov gave the Lightning the lead at 12:12 when he redirected a shot from Eric Brewer beneath the glove of Holtby.
"There was a lot of back-and-forth momentum tonight," Lightning forward Ryan Callahan said. "I think we did a good job of holding on when they had the momentum. It definitely wasn't the prettiest of victories, but we got two points from a pretty good hockey team. Right now we'll take it and try to finish strong."
"We've had a lot of good chances in the last couple of games where we lost a few of them," Brouwer said. "Our scoring touch just isn't there. We're getting lots of chances, we're getting lots of looks, and we just have to find ways to bury teams."
Callahan, who missed the past five games with a lower-body injury, scored in the first period when he directed a pass from Brian Boyle between Holtby's pads. Johansson tied the game at 12:59 when he scored on a rebound of a shot by Alex Ovechkin. The assist ended Ovechkin's career-long five-game pointless streak.
"It was good to get back playing and good to get a positive result kind of early when you're coming back from injury," Callahan said. "It calmed me down a little."
Bishop had 35 saves for the Lightning. Holtby had 24 saves for the Capitals, who host the Arizona Coyotes on Sunday.
"Last couple of games we've played good hockey and haven't gotten the results," Capitals center Nicklas Backstrom said. "You have to battle through it and we have a new game tomorrow. Sometimes that's hockey, it's important that we stick together as a group."
Lightning wing Alex Killorn left the game in the second period with an upper-body injury and did not return.