It would prove to be the only goal of the period, and the Habs headed to the room with a 1-0 lead despite being outshot 12-6 after 20 minutes.
The second period was largely uneventful on the scoresheet until late in the frame, when Calgary tied things up when Elias Lindholm one-timed Jonathan Huberdeau's cross-crease pass past Allen with 29 seconds remaining.
The score was tied at 1-1 through two periods, with the Flames outshooting the Habs 13-8 in the second.
The Habs retook the lead at 6:29 of the third. With Andrew Mangiapane in the box for roughing, Caufield ripped a one-timer from his office at the faceoff dot to Markstrom's right to make it a 2-1 game.
The goal, scored on the power play, was the 40th of Caufield's career and his 13th of the season. Nick Suzuki, the author of the cross-ice pass, and Monahan got the assists.