Tomas Fleischmann added two goals and two assists for Washington, which won its second straight game. The Capitals hadn't won consecutive games since beating Atlanta and Philadelphia on Jan. 6 and 9.
Boyd Gordon also scored for Washington and Alexandre Giroux got his second NHL goal. His first came in Friday's 5-1 win over Toronto.
The Capitals are 2-0-1 since goalie Olie Kolzig returned Thursday after missing 13 games with a knee injury. Kolzig made 30 saves against the Lightning.
Filip Kuba scored a power-play goal for Tampa Bay.
An early Toronto miscue helped the Capitals take the lead Friday, and a Tampa Bay mistake gave Washington another first-period gift Sunday.
Defenceman Dan Boyle lost the puck near the blue line, and Fleischmann then beat goalie Johan Holmqvist near the left circle for a 1-0 lead at 5:31.
Fleischmann made it 2-0 with 6:20 left in the period on a long slap shot. Tampa Bay coach John Tortorella pulled Holmqvist for Marc Denis a few minutes later.
Semin then scored on the first three Washington shots of the second period.
He scored a power-play goal at 1:14, converted a backhander at 6:45 and scored on a long wrist shot 8:18 into the period for a 5-0 lead. The fans then littered the ice with hats, and Tortorella put Holmqvist back in, but the damage was done.
Notes: Fleischmann also scored the final Washington goal in Friday's win over Toronto. ... The Capitals have outscored opponents 6-0 in the first period of their last three games. ... Tampa Bay had won five of the first six games with Washington this season. ... Six of Kuba's 11 goals have come on the power play.