Lecavalier has a career-high 39 goals, three shy of Brian Bradley's team record set during the 1992-93 season. Lecavalier has scored a goal in 15 of 19 games.
Washington's Dainius Zubrus forced overtime when he scored from the slot after a turnover by Tampa Bay with 14.9 seconds left in the third.
The Lightning, who appeared earlier this season in jeopardy of missing the playoffs just three years after winning the Stanley Cup, have won 14 of 17 and are one point behind the Southeast Division-leading Atlanta Thrashers.
Alexander Semin also scored for the Capitals, who have lost 11 of their last 12 road games. Washington played for the first time without injured goalie Olie Kolzig, who hurt his knee in practice Monday and is expected to miss at least three weeks.