Matvei Gridin backhanded a pass from behind the goal line out to the slot to Strome, who swatted the puck past Tampa Bay goalie Jonas Johansson.
Pontus Holmberg tied it for the Lightning at 15:40 of the third period. Yanni Gourde passed the puck out front from behind the goal line to Holmberg in the slot, who chipped it over Cooley’s blocker.
Victor Olofsson, Morgan Frost and Mikael Backlund also scored for the Flames (29-34-7), who have won three straight games. Devin Cooley made 32 saves.
Ryan McDonagh and Darren Raddysh also scored for the Lightning (43-21-5), who are 3-0-1 in their past four games. Johansson made 25 saves.
McDonagh gave the Lightning a 1-0 lead at 7:25 of the first period when his wrist shot from the high slot went in off the glove of Flames defenseman Zane Parekh’s glove past Cooley.
Olofsson scored his second goal in as many games at 16:25 to pull the Flames even at 1-1 at 16:25. He took a pass from Yegor Sharangovich and snapped a shot from the left circle to the short side over Johansson’s left shoulder.
Frost scored 27 seconds later at 16:52 to give Calgary a 2-1 lead, taking a backhand pass from Matt Coronato in the left circle before skating towards the net and snapping a shot to the far side past Johansson’s glove.
Backlund made it 3-1 at 8:28 of the second period when he took a pass from Blake Coleman at the blue line and skated to the top of the right circle before letting go a slap shot past Johansson’s glove.
Raddysh scored at 11:47 to pull the Lighting within 3-2. He took a pass from Nikita Kucherov and one-timed a shot from the top of the right circle past Cooley to the short side.
Kucherov has 13 points (six goals, seven assists) on a four-game point streak and leads the NHL with 119 points (40 goals, 79 assists).
Coleman appeared to put Calgary up 4-2 with a wrist shot from the left post at 19:48, but the call was reversed following a successful challenge for offside.
