Alex Frolov and Brian Boyle also scored for New York. Martin Biron, signed in the offseason to back up Henrik Lundqvist, gave up two goals on 19 shots in two periods for the Rangers before Chad Johnson finished up.
Travis Zajac, Ilya Kovalchuk and Zach Parise -- New Jersey's newly formed top line -- each had a goal for the Devils, who fell to 0-2 in the preseason. Martin Brodeur, seeing his first action of the preseason, played the first two periods for New Jersey. He gave up three goals on 27 shots before giving way to Jeff Frazee.
On the winner, Gaborik took a return feed from Frolov and beat Frazee from between the circles for a power-play goal.
Gaborik and Zajac scored as the teams deadlocked at 1 after one period.
Gaborik, who led the Rangers with 42 goals last season, staked New York to an early lead with a power-play tally at 6:43. The goal was set up by a sharp pass across the crease from free-agent acquisition Frolov.
Zajac countered for New Jersey at 13:11, snapping a feed from $100 million linemate Kovalchuk past Biron.
The Rangers, helped by four power plays, dominated the opening period with a 16-9 edge in shots.
Frolov and Boyle scored in the second period as the Rangers took a 3-2 lead.
Frolov notched an unassisted tally at 5:15, capitalizing on the turnover by Matt Taormina, who could not handle a pass from defensive partner Colin White to put the Rangers ahead 2-1.
Kovalchuk deadlocked the score at 2 with an electrifying goal at 12:14. Taking a lead pass from Parise, Kovalchuk slipped behind the Rangers defense to break in alone and rip a shot over Biron's left shoulder.
Boyle gave the Rangers their third lead at 14:21. He used his long reach to elude Devils defenseman Eric Gelinas and poke the puck past Brodeur. That almost stood as the winner until the Devils forced the overtime when Parise scored with 1:46 remaining on a slap shot from the top of the left circle that trickled between Johnson's pads.