The Metropolitan Division match-up was played out in a pulsating atmosphere at Nassau Veterans Memorial Coliseum, with Chris Kreider giving the Rangers an early lead which was overhauled in the second period by Cal Clutterbuck and Peter Regin.
But Derek Stepan's second assist helped McDonagh level the scores on a power-play before Pouliot had the final say.
The New Jersey Devils, sixth in the same division, are just a point behind the second-placed Islanders after winning 2-1 against the Tampa Bay Lightning, who now trail the Toronto Maple Leafs by two points at the top of the Atlantic Division.
The Leafs enjoyed a 4-0 win over the Edmonton Oilers as Phil Kessel scored twice and had assists on James van Riemsdyk and Nazem Kadri's goals.
The Montreal Canadiens moved level with Tampa on 16 points after beating the Dallas Stars 2-1 with goals from Michael Bournival and Rene Bourque and 26 saves by Carey Price.
In the Western Conference, the Chicago Blackhawks are only a point behind Central Division leaders the Colorado Avalanche after a wild 6-5 win over the Ottawa Senators.
Jonathan Toews scored a hat-trick as Chicago came from 4-2 down to lead 6-4 before Zack Smith's consolation counter.
The St Louis Blues are third in the division after a 3-2 win over the Winnipeg Jets, Alexander Steen with the decisive goal.
The Anaheim Ducks came from 2-0 down to beat the Philadelphia Flyers 3-2 and move second in the Pacific Division, Kyle Palmieri settling the game with two goals in the final period.
The Phoenix Coyotes rode Mike Smith's 41 saves to a 3-1 win over the Los Angeles Kings.