"I'm feeling more comfortable," said Monahan, Calgary's first-round pick (No. 6) at this year's NHL Draft.
Evgeni Nabokov started in goal for New York and allowed two goals on 16 shots. He was replaced midway through by Ken Reiter.
"They played better than us tonight. They got more bodies and pucks to the net than we did," Islanders coach Jack Capuano said.