Monahan tied it 2-2 at 2:40 of the third period on a rebound in the slot off Travis Hamonic's initial shot. Lindholm got the rebound of his own shot at the top of the crease and beat Koskinen under his arm to give the Flames a 3-2 lead at 9:10.
Lindholm scored into an empty net at 19:18 to make it 4-2.
"It's been off for a couple games here," said Lindholm, who hadn't scored in his previous five games. "We haven't played great. It's good for us to get some goals and get the feel of how to score a goal."
Calgary leads the NHL with 32 goals in the third period and six wins when trailing after two periods.
"For now, it works to be down in the third, but we just talk before the third to give it all and play better," Lindholm said. "A lot of times we play unreal in the third, but you don't want to chase the game too much. It's not going to work all the time to be down before the third. It' something we need to work on."