Hudson Fasching put the Islanders back in front 2-1 at 4:30, cutting to the net around Pietrangelo and stuffing a shot five-hole on Thompson.
Holmstrom, who was playing his 11th NHL game, made it 3-1 at 17:36. After Jean-Gabriel Pageau held the puck in with his skate at the blue line, Holmstrom deked Pietrangelo in the slot and shot five-hole again on Thompson.
"It was just trying to get a shot on net as quick as I could, and luckily it went in," Homstrom said. "It was unbelievable. The teammates I play with are unbelievable, so it's a great thing to share it with them."
Smith scored his second power-play goal through a screen by Mark Stone to cut it to 3-2 at 3:29 of the third period.