"It's a big shot for us," Gulutzan said. "It was one heck of a shot. It enabled us to get a point in tonight's game. That's a big goal. I think that'll be a little bit of a weight off his shoulders. You know how goal-scorers are. They can be streaky, and I think that was a big goal for him."
Monahan had been dropped to the fourth line for the first two periods of the game.
"I think you can always be better, but to put one in tonight … that's going to help me," he said.
Elliott blockered away Shane Prince's breakaway attempt at 11:16 to keep Calgary tied 1-1 midway through the third and force overtime.
"The breakaway at the end was a huge save," Gulutzan said. "I think there was some things in there and things from this road trip we've learned from him and we can take. [Elliott] is a guy that it was a game for him to build off of, too."
Tavares put the Islanders up 1-0 at 7:28 of the first period. He took a drop pass from Josh Bailey and snapped a shot far side over Elliott's shoulder for his first goal since Nov. 3 -- a span of 10 games.
"It's tough when you give up a chance on one of the best players in the world in the slot there," Elliott said. "You have to tip your hat sometimes."
Deryk Engelland nearly tied the game three minutes later. He stepped out of the penalty box and into a partial breakaway, but he couldn't lift a backhand over Greiss' pad.
Greiss also stopped Matt Stajan's partial breakaway after he was sprung by Dougie Hamilton at 15:19 of the second period and Elliott denied Bailey's initial attempt and follow-up whacks after he and Nikolai Kulemin were left uncontested in front of the net with two minutes remaining in the period.
"He played well," Monahan said. "He made some big saves, some key ones. That kept us in the game. We rallied behind him and when he made those big saves we tried to put the puck in the net for him."