Vinny Prospal had a goal and two assists and Ryan Craig also scored for the Lightning, who got 18 saves from goaltender Johan Holmqvist to match a season high with their third straight win.
Alexander Semen scored two goals and Alexander Ovechkin had two assists for Washington, which had won three in a row following a tough stretch in which the Capitals lost seven of eight games.
Lecavalier scored his 25th goal for a 2-1 lead in the first period, then added his 26th after making a nifty move to get the puck around Washington goalie Olaf Kolzig for a 4-3 advantage with 7:36 remaining in the second.
Lecavalier narrowly missed getting a third goal, misfiring at an empty net from the blue-line with about 30 seconds to go.
St. Louis delivered his game-winner less than four minutes into the final period.