WATCH: All Islanders vs. Avalanche highlights
"It was a long time coming," MacKinnon said. "It's been tough at home, it's been tough in general, obviously. Wins haven't been easy to get, and obviously we have a lot of work to do still, but it definitely feels good."
Calvin Pickard made 35 saves for Colorado and ended his five-game losing streak.
"Huge relief," he said. "It's tough to get out of a streak when you're losing every game at home. We weren't playing with a whole lot of confidence. Hopefully this builds some of that and we can string some wins together. It's been a long time, it's been tough. We're still in a huge hole. Just getting a win was big.
"Losing in overtime wouldn't have been great. It's nice to get a [positive] result. I thought I'd been playing pretty decent the past few games and not [getting] much results."
Greiss made 37 saves for the Islanders (15-15-7), including one against Matt Nieto on a penalty shot at 14:16 of the first period and against Rene Bourque on a breakaway in overtime.
The Islanders last played Dec. 31, a 6-2 win against the Winnipeg Jets. They are 4-1-1 in their past six games.
"I think we played pretty hard, especially coming out of a break," Greiss said. "We fell behind pretty quick, but we responded good after the goal we gave up. I think we played a pretty good game and just got a little bit unlucky and we didn't score."
The Avalanche took a 1-0 lead at 6:06 of the first period on a goal by Gabriel Landeskog, his first in five games and seventh of the season. Landeskog moved to the top of the left circle and beat Greiss to the glove side.
The Islanders tied the game 1-1 on defenseman Johnny Boychuk's goal at 17:34 of the second period during a 5-on-3 advantage with Fedor Tyutin (hooking) and Nikita Zadorov (cross-checking) in the box. Nick Leddy made a short pass to Boychuk, who put a shot from the high slot by Pickard's glove for his fifth goal and first in 12 games.
