The Canadiens will try to avenge that overtime defeat in Tuesday night's rematch and improve to 2-0-0 on their longest road trip of the season.
Montreal (14-4-4) is 8-0-3 in its last 11 games, including a 4-3 loss to the Islanders on Feb. 21 in which New York (9-11-2) rallied from an early two-goal deficit. Rookie defenseman Thomas Hickey's only NHL goal and point ended that game.
The Canadiens quickly bounced back from that defeat and did the same following another overtime loss this weekend. After falling 7-6 to Pittsburgh on Saturday, Montreal scored two goals in the third period for a 4-3 win at rival Boston the next day to take over sole possession of first place in the Eastern Conference.
David Desharnais tallied the tiebreaking goal with 10:43 remaining -- his second of the game -- while Max Pacioretty scored his fourth in three contests in the opener of a five-game trek.
"We've given up some leads this season and it's usually from sitting back and being too conservative. That's something we talked a lot about," forward Brandon Prust told the team's official website. "We wanted to keep on them and keep pressuring them and playing in their zone as much as we could and it worked well tonight."
Pacioretty, the NHL's first star of the week, has eight goals and six assists over his last nine games and scored twice in the loss to the Islanders.
"A lot of this is my teammates and linemates," he said. "They're finding me and they've been doing a lot of the hard work. I think they're getting rewarded as well."
Pacioretty has seven goals and an assist in his last six games against New York and recorded his only career hat trick in Montreal's most recent visit to Long Island, a 4-2 win Feb. 9, 2012.
New York lost nine of its first 11 at home this season before a 3-2 shootout win over visiting Ottawa on Sunday. An ill John Tavares had the winning shot in the tiebreaker after the Senators pulled even with 1:09 remaining in regulation.
"We can do better," coach Jack Capuano said. "This game is over and now we're focused on Montreal for Tuesday. We have to try to be better every day."
That could be a challenge Tuesday considering Montreal is 5-0-1 in its last six road games. Carey Price, who could be back in net after Peter Budaj beat the Bruins, is 5-0-1 with a 1.29 goals-against average in opponents' arenas on the season.
New York, though, has won five of the last seven meetings with the Canadiens, including two straight. Matt Moulson scored twice on the power play in last month's victory to give him five goals in his last five games in the series.
Since that contest, the Islanders are 1 for 15 with the man advantage and haven't scored on their last 11 opportunities. The Canadiens have killed off 20 of their opponents' last 23 power-play chances and seven of eight over the past five games.