Charlie Coyle had two goals, and Ullmark made 27 saves for the Bruins (34-12-12), who extended a road point streak to 11 games (7-0-4).
"You want two points," Coyle said. "We had chances to end the game. That's hockey. It's an inch or two there and it's a different story and we're feeling great about our game. I thought for the most part we played pretty solid. It stings a little bit when you don't capitalize and get two points but we worked our way and some things we can definitely look at and build on. It was right there."
Kylington, who missed all of last season and the first three months of this season to attend to his mental health, shot low glove by Ullmark from the high slot to put Calgary up 1-0 at 12:55. It's his second goal in as many games.
Coyle tied it 1-1 at 18:41. Markstrom came out of his net to play the puck but couldn't clear it out of the zone past Coyle, who shot by the Flames goalie before he could retreat back into his crease.
Pospisil restored Calgary's lead 42 seconds later, poking a rebound on Connor Zary's backhand over the goal line to make it 2-1 at 19:23. The goal is Pospisil's first since Dec. 18, a span of 20 games.