Following a scoreless first round in the extra segment, Park beat Carey Price past his glove and above his shoulder, and after Montreal's Alex Tanguay faltered, Bill Guerin put it away by also beating Price to the glove side.
Park also scored in regulation for the Islanders, who have won five of their last six games. Doug Weight tallied two assists, while Joey MacDonald stopped 23-of-26 shots in the win for New York.
"It's an unfortunate bounce for Price, he had a good game going," MacDonald said. "Fortunately enough, we killed the penalty with a minute and some left in the game. It's good to get that second point in the shootout, too, after battling back."
Steve Begin, Josh Gorges and Maxim Lapierre scored for the Canadiens, who have lost three of four. Price allowed three goals on 24 shots in the loss.
Montreal led 3-2 with about five minutes to play, and a delayed penalty on New York allowed Price to leave the net in favor of an extra attacker. The plan backfired, however, as defenseman Ryan O'Byrne mistakenly sent a pass back toward the net, and the puck went into the empty net. The goal was credited to Guerin.
"The puck chipped off the boards, I went back to get it and play it back to (Price)," O'Byrne said. "And, obviously, (Price) wasn't in the net. It's an unfortunate circumstance, but I am facing the music. The fans were chanting my name at the end of the game, but hey, tomorrow's another day."
The Islanders took an early lead on the power play in the first. After Price saved a flurry of shots, Park got a clear shot in the slot and blasted it over the sprawled netminder at 6:54.
But the Canadiens came back 17 seconds later to tie the game. A wrist shot from the point was deflected nicely out in front by Begin and the puck found its way into the back of the net.
Montreal grabbed the lead later in the first on the man advantage. After a pass from Alex Kovalev, Gorges sent a slap shot from the point through traffic, and the puck snuck past MacDonald at 9:58.
The Canadiens made it a two-goal game early in the second. Fresh off a power play chance, Robert Lang passed it through two defenders to Christopher Higgins, who dished it across the crease to Lapierre. Lapierre beat MacDonald before the netminder could slide over at 4:29.
New York came back to make it 3-2 soon after. Joshua Bailey's shot from the right circle went off the post and bounced back out to Trent Hunter, who hit the post; however, the puck bounced off of Price's glove and into the net at 8:05.