Mikka Kiprusoff made 14 saves for the Flames (5-0-0), and Leland Irving gave up one goal on seven shots in the third period.
"I thought it was somewhat sloppy at times," Calgary coach Darryl Sutter said. "I didn't think we played a pretty strong game here. That being said, we also did some things that were key at different moments."
Calvin de Haan and Trevor Gillies scored for the Islanders (0-2-0), who played their first two preseason games Wednesday. New York's other split-squad lost 3-1 in Philadelphia.
"There's a little bit of rust, but considering we're playing a team that's been playing a few games, there's a lot more positive than negative," New York coach Scott Gordon said.
"It's not like we need a major overhaul -- it's our first game. We weren't perfect, but they've played five games and have been far from perfect so we're not going to complain."
Meyer scored two minutes into the second when he deflected Adam Pardy's shot past Rick DiPietro. Glencross then got loose in the Islanders zone and knocked in his own rebound.
DiPietro's woes continued when his clearance attempt bounced off Kotalik and into the net to give the Flames a 3-0 lead.
De Haan scored a power-play goal in the second, and Gillies converted early in the third.
DiPietro made 13 saves before giving way to Mikko Koskinen in the third period.
The Islanders continue their preseason schedule Friday at New Jersey. The Flames take on the Oilers in Edmonton on Friday.
Copyright by STATS LLC and The Associated Press
No scoring this period
Stefan Meyer 1 Assist: Adam Pardy
Curtis Glencross 1 Assist: Ian White, Mark Giordano
Ales Kotalik 3 Unassisted
Calvin de Haan 1 (power play) Assist: Rob Schremp, James Wisniewski
Trevor Gillies 1 Assist: Rhett Rakhshani, David Ullstrom