Jagr opened the scoring 4:47 into the game, immediately dispelling any doubts about the status of the wrist he broke last month. After carrying the puck along the right boards, he maneuvered around defenseman Stan Neckar and flicked a shot past goaltender Nikolai Khabibulin.
"We jumped on them in the first period," Jagr said. "They had some chances and we stopped them, and things started to settle down. I just try to get 1-on-1. That's what I am always looking for. When I have it, I am always going to go for it."
The All-Star winger, helped double Washington's lead just under 2 1/2 minutes later by setting up the first of Peter Bondra's two goals.
"They tried to double-team Jagr sometimes, and that's when I jumped into the hole and took the puck to the net," Bondra said.
Jagr struck again with 76 seconds left in the period to restore the Capitals' two-goal lead after Vaclav Prospal put Tampa Bay on the board. Taking advantage of a goalmouth scramble that left Khabibulin sprawling, Jagr collected a pass from Robert Lang in the left faceoff circle and snapped it into a half-empty net.
Jagr also picked up an assist on Michael Nylander's power-play goal 99 seconds into the second period, tying his playoff career high for points. He also had four for the Pittsburgh Penguins in a 7-0 rout of Washington on April 13, 2000.
Bondra, who chipped in an assist, also equaled playoff career highs for goals and points.
Goaltender Olaf Kolzig made 40 saves for Washington, which hosts Game Three on Tuesday.
Fredrik Modin and Dave Andreychuk had the other goals for the Lightning, who have not recorded a postseason home win since April 21, 1996.
With his team giving up seven power plays, Khabibulin stopped 24 shots and surrendered as many as five goals for just the fifth time this season.
"They've been right on top of us and a step ahead of us," said Tampa Bay defenseman Dan Boyle. "It's tough to play catch-up hockey against guys like Jagr, Bondra and Kolzig."