Milan Lucic gave Calgary a 1-0 lead at 4:36 of the first period on its first shot, a one-timer on a cross-slot feed from Jonathan Huberdeau over Varlamov's glove.
Coleman made it 2-0 at 6:05 when he tucked in his own rebound from a sharp angle.
Nikita Zadorov extended the lead to 3-0 at 14:41 after one-timing a shot from the point over Varlamov's glove.
"It was a good start for the group, I thought," Coleman said. "Six shots in the first isn't ideal, but capitalized on our opportunities, which has been a bit of a miss for us in some of these games. Good to get rewarded on a few chances. Obviously, that gave us the start we needed."
Parise cut it to 3-1 at 19:00, puck-handling around Zadorov before firing a shot top-corner over Markstrom's glove.
"I don't think by any means we felt like we were getting outplayed," Parise said. "We had our looks in the second, couple breakaways, couple chances in the slot. Had some chances in the third again, didn't convert.
"I don't think as a whole we played that bad of a game. I think we played hard, we competed. We need the result, but we didn't get it."
Markstrom made a pad save on Casey Cizikas on a breakaway at 10:05 of the second period, eight seconds after his hooking minor expired, and a stick save on Jean-Gabriel Pageau's short-handed break at 10:46.
"It was huge because I think at that point, especially first and second breakaway, I don't think we were having a very good period at the time and he kept it a two-goal lead going into the third," Lucic said. "It's good to see him finding confidence in his game as well, and we need him to be good every night to give us a chance to win."