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."
