Yegor Sharangovich, Justin Kirkland and Yan Kuznetsov also scored for the Flames (21-23-4), who have won two games in a row and three of their past four. Kevin Bahl had two assists, and Dustin Wolf made 28 saves for his first win in his past six starts.
Jean-Gabriel Pageau and Anders Lee scored for the Islanders (26-17-5), who are 2-2-1 through five games of a seven-game road trip. Matthew Schaefer had two assists, and David Rittich made 15 saves.
Sharangovich put the Flames up 1-0 at 11:51 of the first period when he took a pass in the high slot from Rasmus Andersson and lifted a shot high to the glove side. Sharangovich scored for the second straight game and has a three-game point streak (two goals, three assists).
Klapka made it 2-0 at 3:04 of the second period when Bahl’s wrist shot from the right point deflected off his stick and his leg past Rittich.
Kirkland scored his first goal of the season at 9:50 to extend Calgary’s lead to 3-0. He skated down the right wing on a 2-on-1 and took a pass from Ryan Lomberg before roofing a shot past a sprawling Rittich.
Kuznetsov made it 4-0 at 11:49 with a wrist shot from the left point to the top right corner. Connor Zary had the secondary assist on the goal to extend his point streak to a career-high five games (two goals, four assists).
Pageau scored from the left circle just 32 seconds later, lifting a shot to the short side to make it 4-1 at 12:21.
New York coach Patrick Roy pulled Rittich for an extra attacker with 8:04 remaining in the third period. Lee then cut it to 4-2 at 17:04 with his 300th NHL goal and first in 10 games, squeezing a shot from below the left circle through Wolf’s pads.
He became the fifth player to score 300 goals with the Islanders, alongside Mike Bossy (573), Bryan Trottier (500), Denis Potvin (310) and Clark Gillies (304).
