New York won its fifth straight and handed the Senators their fourth consecutive setback.
The Rangers played their first road game in two weeks, having gone 4-2 during their opening homestand of the season. New York played its first seven contests away from home this season, two of them in Europe.
Milan Michalek put Ottawa in front 8:39 into the second period, but Gaborik tied it 42 seconds later.
Derek Stepan scored on a backhander with 8:22 to go in the second to give the Rangers the lead for good and Gaborik gave New York some insurance 8:30 into the third. Gaborik has nine goals for the season, two off the league lead.
Nick Foligno brought the Senators within one midway through the third, but they could not put another one past Henrik Lundqvist.
Lundqvist, who has been in goal for three of the five consecutive wins, stopped 28 shots.
Craig Anderson made 15 saves in taking the loss.