Josh Bailey, Matt Moulson and Frans Nielsen each had a goal and an assist for the Islanders, who dropped their season opener to Dallas on Saturday. Rick DiPietro stopped 29 shots in the win.
Michael Del Zotto, Brandon Dubinsky and Artem Anisimov each had a goal and an assist for the Rangers, who had opened their season on Saturday with a 6-3 win over Buffalo. Henrik Lundqvist was charged with five goals on 31 shots.
The score was tied going into the third period and the Rangers took the lead with 7:14 to play. Marian Gaborik skated the puck around the left side of the net and from the mid-boards backhanded a pass to the left circle where Anisimov one-timed a shot past DiPietro for a 4-3 lead.
Ryan Callahan and Marc Staal, though, took penalties 46 seconds apart and the Islanders went ahead with two power-play goals.
On the 5-on-3, a slap shot from the left point by James Wisniewski was blocked in front with the puck going to the left side where P.A. Parenteau banged it home with 4:24 left in regulation.
Less than a minute later, Bailey sent a turnaround backhand pass from the right side to the slot where Comeau one-timed it home for a 5-4 advantage.
The Rangers pulled Lundqvist for the extra attacker and got several quality chances, but DiPietro came up with the saves and Nielsen’s empty-netter sealed the win.
Gaborik was awarded a penalty shot 11:08 into the first when he was hauled down on a breakaway by Doug Weight, but his wrister was easily turned aside by DiPietro.
The Islanders scored 1:39 later as Del Zotto lost the puck in his own zone, Comeau picked it up down low and his second shot got past Lundqvist for a 1-0 lead.
The Rangers answered just over a minute later on the power play when Dubinsky followed up his own blocked shot with another wrister past DiPietro for his third goal of the young season.
The Islanders, though, took a 2-1 lead into the first intermission when a turnover at the Rangers blueline resulted in the puck going down low where Bailey grabbed the loose puck and his quick shot went off the left post and in with 3:13 left in the frame.
The Rangers tied the game 8:28 into the second with a power-play marker as Del Zotto’s shot from the right point hit off the stick of an Islander in front.
About 4 1/2 minutes later, the Rangers took their first lead of the game. Just moments after a power play ended, Dan Girardi’s wrister from the top of the right circle squeezed inside the right post for a 3-2 lead.
However, the Islanders evened the score in the waning moments of the second frame. Trent Hunter slapped a shot wide of the net that took a hard bounce off the back boards and came back out to the left side. Lundqvist tried to push it away with his stick, but the puck went right to Moulson and he chipped it in.
The Islanders play at Washington on Wednesday…The Rangers open up the home portion of their schedule on Friday against Toronto…Each team won three times in the series last season…The Rangers went 2-for-4 on the power play while the Islanders finished the game 2-for-5.