Jonathan Drouin and Emil Heineman scored and David Rittich made 27 saves for the Islanders (10-6-2), who have won four games in a row, the past three in overtime.
“I think it was a character win in a way that we found a way to win a hockey game where things were not going our way at the beginning,” Islanders coach Patrick Roy said.
JJ Peterka and Dylan Guenther scored, and Vejmelka made 19 saves for the Mammoth (10-7-1), who have lost four of their past five games.
“We had a really good first period, and for a number of reasons, we lost our momentum in the second period,” Mammoth coach Andre Tourigny said. “I think we were on our heels too much in the third period. We were protecting the lead, but we did not have the same aggression.”
Heineman opened the scoring at 7:13 of the first period, scoring a 4-on-4 goal by swatting a backhand with his back to the net to give the Islanders a 1-0 lead.
Nick Schmaltz appeared to have tied the game for Utah at 11:41, but after video review it was determined that the puck never crossed the goal line and was ruled no goal.
Peterka scored at 13:02, tapping in a pass from Lawson Crouse to make it 1-1.
Guenther scored a 5-on-3 power-play goal at 18:35, firing a one-timer past Rittich to give the Mammoth a 2-1 lead.
“We didn't have a very good first period, that's for sure,” Roy said. “I'm so proud of them because they came back in that second and we started placing the puck behind their defense. We managed the puck so much better. I thought we got some momentum out of that second period and in the third, we got a goal by Drouin, which was a big one.”