The Rangers took a 1-0 lead into the first intermission thanks to a Lafreniere goal on a two-man advantage.
But the Flames were not without chances of their own. Coronato found himself in alone on goal after accepting an entry pass from Morgan Frost on his first shift of the game, but after navigating across the crease, he was unable to tuck the puck past the outstretched pad of Rangers starter Jonathan Quick.
Yegor Sharangovich got a short-handed breakaway, too, 10 minutes into the game, but his snapshot from the slot struck the crossbar and sailed out of play.
New York extended its lead at the 10:28 mark of period two on a Conor Sheary goal, then Lafreniere notched his second of the game six minutes later, capping off a three-way passing play with a tap-in at the right post.
Coronato had another glorious chance late in the third period, after he found himself alone with the puck in tight, but his shot slid past a prone Quick and just wide of the left post.
Lafreniere completed his hat-trick with 2:18 to play.
