The Capitals stopped a six-game losing streak behind Kolzig, who turned aside 16 shots in the first and 23 of 25 during the third. Washington is 4-0-2 when allowing 40 or more shots this season. Kolzig made 20 or more saves in the four victories.
Kris Beech, Boyd Gordon, Chris Clark and Alexander Ovechkin also scored for the Capitals, who had been outscored 25-9 during their skid.
Nick Tarnasky and Vincent Lecavalier scored third-period goals for the Lightning, who lost for fourth time in 11 games.