Washington won its second in a row and its league-best 16th of the campaign. The Capitals moved one point ahead of Philadelphia for the top mark in the NHL.
Semin scored Washington's third, fourth and fifth goals, all of them coming in the second period and two of them coming on the power play. He has 17 goals for the year.
The other scores came from John Carlson, John Erskine and Tom Poti.
Tampa Bay goaltender Mike Smith was removed from the game after giving up four goals on 18 shots. The Lightning had a five-game winning streak snapped.
Semin also had a hat trick against Atlanta on Oct. 23 and Tampa Bay on Nov. 11. Varlamov's shutout was his first of the season and the third in his 36 NHL appearances.