The Rangers won their third in a row and moved within two points of Philadelphia for the lead in the Atlantic Division. The Islanders had won two straight.
Gaborik gave the Rangers the lead with his 20th goal of the season. Steven Stamkos of Tampa Bay and Jonathan Toews of Chicago began the night as the only players in the NHL with 20 goals.
Michael Del Zotto gave the Rangers a 3-1 lead after two periods, but Matt Moulson brought the Islanders back within one with a power-play goal 8:29 into the third.
It remained a one-goal game until John Mitchell scored into an empty net with 1:33 remaining.
The cross-town rivals had split their previous two meetings this season.
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