The Flames had chances to take the lead in period one, notably a rebound opportunity from Mikael Backlund, and a breakaway chance from Andrei Kuzmenko which both went begging.
At the other end, Wolf made nine saves in period one, but he also took time to thank his post; after it kept a Brad Marchand drive out with nine seconds left on the clock.
Marchand clanked a second shot off the pipe a minute and a half into the second period, and the score stayed level for several minutes.
But Boston broke the game open with a pair of quick strikes just before the midway mark of the frame.
Pavel Zacha took advantage of a fortuitous bounce that fell to his stick in the high slot, slapping the puck home at 8:25 to give the Bruins a 2-1 lead.
Cole Koepke extended the advantage 31 seconds later, tapping the puck in at the left post after a cross-crease pass from linemate Charlie Coyle.
Wolf made two key stops before the period was through, one off a Pastrnak partial break, the other a re-direct from in tight by former Flames teammate Elias Lindholm with about five minutes on the clock.
Boston outshot Calgary 14-13 in period two.