Andrei Vasilevskiy made 29 saves, and Nikita Kucherov had two assists for Tampa Bay, the No. 2 seed in the East, which leads the best-of-7 Stanley Cup Playoff series 3-1.
"The talent they have over there, they're an exceptional team," Lightning coach Jon Cooper said of the Bruins. "They had to play a lot of their players a bunch of minutes to get themselves back into it. We weathered the storm when they were pressing. … On our side of things, guys were committed. Guys were blocking shots. Guys were committed to our structure in the neutral zone."
WATCH: [All Lightning vs. Bruins highlights]
Jake DeBrusk scored, and Jaroslav Halak made 23 saves for Boston, the No. 4 seed, which has lost three straight games. The Bruins have been outscored 10-2 in the past two games, including 7-1 in Game 3 on Wednesday.
"The other day, I do feel those games happen from time to time where the other team is better and they take advantage of opportunities," Bruins coach Bruce Cassidy said. "They keep getting opportunities and taking advantage of them. So I don't think we had our legs in Game 3. This one, I thought we did. We had our energy level.
"We were competing hard, winning our share of races, winning pucks. To score goals, we have to hit the net more often."
The game was rescheduled from Friday after the players on the eight remaining teams decided not to play as a form of protest against systemic racism and police brutality.
Game 5 is in Toronto, the East hub city, on Monday (7 p.m. ET; NBCSN, CBC, SN, TVAS).
Teams that have a 3-1 lead are 284-29 (90.7 percent) winning a best-of-7 NHL series, including 6-0 this postseason.
Palat put the Lightning ahead 1-0 at 8:59 of the first period with a snap shot before scoring on a one-timer from the high slot, making it 2-0 at 12:29 of the second. He has four goals in three games after having a goal and an assist in Game 3, and scoring in overtime of a 4-3 win in Game 2.