[WATCH: All Capitals vs. Lightning highlights | Complete Lightning vs. Capitals series coverage]
The Lightning are the first team to win a game at home in the series. They have won three games in a row after losing Games 1 and 2 at home.
Game 6 of the best-of-7 series is at Washington on Monday.
"Our whole coaching staff in team meetings, the message was, 'It doesn't really matter how you get there,'" Lightning defenseman Ryan McDonagh said. "That was a good job by us putting behind what wasn't good for us in the first two games and trying to find a recipe for success and trying to go out and execute that plan as close as we could to 60 minutes. We've gotten close to that 60-minute game, and tonight was obviously, I think, the best step in the right direction there, but it's only three-fourths of the way done. Next one is going to be a lot of fun but a huge challenge."
Video: WSH@TBL, Gm5: Palat wires wrister past Holtby
The Lightning got goals from fourth-liners Cedric Paquette and Ryan Callahan, who had an assist for his first multipoint game in the 2018 Stanley Cup Playoffs. Ondrej Palat also scored, and goalie Andrei Vasilevskiy made 28 saves, including 24 in the second and third periods.
Evgeny Kuznetsov and Alex Ovechkin scored, and Braden Holtby made 19 saves for the Capitals.
The team that wins Game 5 in a best-of-7 NHL series that was tied 2-2 has gone on to win the series 79.6 percent of the time (215-55). However, the Lightning had a 3-2 lead in the conference final against the Pittsburgh Penguins two years ago and lost in seven games.
"We just have to win two games," Ovechkin said. "Our goal is to come back here and play a Game 7."
Ovechkin scored a 6-on-5 goal with 1:36 remaining in the third period to cut the Lightning lead to 3-2.
The Capitals continued to pressure after that, but the Lightning had three blocked shots and Vasilevskiy made three saves, including one on defenseman John Carlson on a backdoor play from the left side with 10 seconds remaining.
"Laser focus by our guy," Tampa Bay coach Jon Cooper said of Vasilevskiy's save on Carlson. "You need the big save at the end when you're holding on to a one-goal lead, and he gave it to us. The team propelled us to that lead in front of him, and he gave it to us, closed it out in the end."
Paquette gave the Lightning a 1-0 lead 19 seconds into the game after Capitals defenseman Dmitry Orlov turned over the puck in the neutral zone. Callahan knocked the puck around defenseman Matt Niskanen on the left-wing wall, and then moved it to Paquette, who beat Holtby on the glove side from the left hash marks.
It was Paquette's first goal of the playoffs.
"The roof nearly came off when we scored that first goal," Cooper said. "You could see our team got a little taller on the bench."
Palat made it 2-0 at 9:04 of the first period by scoring with a blocker-side wrist shot from above the hash marks after another Orlov turnover in the neutral zone.
The Lightning outshot the Capitals 13-4 and had a 29-8 advantage in shot attempts in the first.
"To have anything but the effort we had in that first period was unacceptable," Cooper said. "The guys knew it, and that obviously propelled us to what we did tonight."
Callahan scored 33 seconds into the second period to increase the lead to 3-0. Stralman went around Niskanen and got two shots on Holtby. The second rebound popped into the air, and the puck went in off Callahan's right hand after Niskanen played it.
The goal was confirmed after video review.
The Capitals made it 3-1 on Kuznetsov's goal at 4:21.
Washington outshot Tampa Bay 26-9 in the final 40 minutes.
"This group has responded all year," Capitals coach Barry Trotz said. "I don't expect anything different."
Video: WSH@TBL, Gm5: Ovechkin pots one-timer late in 3rd
Goal of the game
Paquette's goal at 19 seconds of the first period.
Video: WSH@TBL, Gm5: Paquette gives Lightning early lead
Save of the game
Vasilevskiy stopping Carlson at 19:50 of the third period.
Video: WSH@TBL, Gm5: Vasilevskiy stones Carlson late in 3rd
Highlight of the game
Callahan's goal at 33 seconds of the second period.
Video: WSH@TBL, Gm5: Callahan scores 33 seconds into 2nd
They said it
"A lot of people counted us out when we were down 0-2 (against the Columbus Blue Jackets) in the first round. Things got hard in the last series (against Pittsburgh) and we could have melted, and we just kept playing. So that's what we've got to do again. Bring our best effort for Game 6 at home, win a game, and then we'll go from there. But we're focused on bringing our best game of the season for Game 6, and we'll be ready to go." -- Capitals defenseman Matt Niskanen
"We have a lot of unfinished business. This isn't even close to being over. This last game is definitely the hardest. Against a very, very good Washington team and to go in their building and try to close them out, it's going to be tough." -- Lightning forward Ryan Callahan
Need to know
The Lightning went to the Stanley Cup Final in 2004 and 2015. They defeated the Calgary Flames in seven games in 2004 after falling behind 3-2 in the series. They lost to the Chicago Blackhawks in six games in the 2015 Cup Final. ... Callahan ended a nine-game point drought dating to Game 5 of the first round against the New Jersey Devils on April 21, when he scored a goal. ... Kuznetsov set the Capitals record for most points in a single postseason (22; 11 goals, 11 assists). Ovechkin had 21 points in 2009.
Game 6 of Eastern Conference Final at Capital One Arena on Monday (8 p.m. ET; NBCSN, CBC, SN1, TVAS)
Video: Lightning edge Capitals in Game 5 to take series lead
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