Ryan McDonagh had two assists, and Andrei Vasilevskiy made 26 saves for the Lightning (23-8-5), who are 8-0-1 in their past nine home games but were 1-2-1 in their previous four overall.
Dillon Dube scored for the Flames (17-9-6), who have lost six of their past eight. Dan Vladar made 29 saves in his first start since Dec. 7.
"I just thought they were a lot quicker than us and made a lot more plays," Calgary forward Matthew Tkachuk said. "Defensively they didn't give us much and their goalie was solid when he needed to be."
Corey Perry gave the Lightning a 1-0 lead at 12:21 of the second period after he chipped the puck past Vladar off a pass from Pierre-Edouard Bellemare. It was Perry's fourth goal in his past six games.
"I thought we played really well," Perry said. "We limited their chances in the first couple of periods. We were on top of them. We were hard, we were physical. We didn't allow any odd-man rushes. It's a good recipe."
Brayden Point extended the lead to 2-0 at 2:52 of the third period when he scored at the left post off a cross-ice pass from Kucherov.
"It was nice to be back, that's for sure," Kucherov said. "It's never easy [coming back from injury], it's getting tougher and tougher."
Ondrej Palat made it 3-0 at 10:10 of the third when he scored in the low slot off Kucherov's pass from below the goal line. Alex Killorn made it 4-0 14 seconds later at 10:24.
"[Kucherov] made some plays out there ... that second goal to set up 'Pointer' ... that's elite," Cooper said. "He's probably only going to get better here when he gets his legs under him."