Ondrej Palat scored twice in the first 3:19 of the game, and the Lightning beat Boston 4-1 to open a 2-1 lead in their Eastern Conference semifinal series.
Andrei Vasilevskiy stopped 28 shots for Tampa Bay, which has won two straight since losing the series opener at home.
Anthony Cirelli scored his first career NHL playoff goal with an assist from Yanni Gourde, whose wife gave birth yesterday giving Tampa Bay a 3-1 lead late in the first.
Patrice Bergeron scored his fourth goal of the playoffs for Boston, and Tuukka Rask made 33 saves.
Game 4 is tomorrow night, again in Boston.