The forward, who was acquired by Calgary in a trade with the Colorado Avalanche on March 6, had one assist in six games entering Friday.
Joel Farabee, Morgan Frost and Matt Coronato also scored for the Flames (28-34-7), who have won two in a row to start a six-game homestand. Blake Coleman had two assists, and Dustin Wolf made 24 saves.
A.J. Greer scored the lone goal for the Panthers (34-32-3), who have lost three of four, all on a road trip that ended Friday .
Farabee gave the Flames a 1-0 lead at 7:44 of the second period. His shot from the left boards deflected off the leg of Panthers defenseman Niko Mikkola in the left face-off circle and over Tarasov's right shoulder into the net.
Olofsson made it 2-0 at 10:10. Adam Klapka sent a pass from below the goal line to Olofsson, who buried a slap shot from the left circle to the glove side.
Greer cut the deficit to 2-1 at 4:17 of the third period with a wrist shot from the left circle over Wolf's glove.
Flames forward Connor Zary left the game at 11:14 after being hooked and then pushed head-first into the boards by Greer, who was given a minor penalty for hooking, a five-minute major for interference and a 10-minute game misconduct.
Mikkola left the game at 12:49 after a knee-on-knee collision with Calgary forward Ryan Strome.
Frost made it 3-1 during a 5-on-3 power play at 16:59, backhanding a loose puck over a sprawling Tarasov from the top of the crease.
Coronato pushed the lead to 4-1 with a power-play goal just 31 seconds later at 17:30. He took a stretch pass from Matvei Gridin in stride into the offensive zone and beat Tarasov with a snap shot from the slot.
