Panarin, who also recorded a hat trick against the Rangers while playing for the Chicago Blackhawks in 2016, notched his fourth career four-point game.
Alexander Wennberg and defenseman Markus Nutivarra also scored for Columbus while Sergei Bobrovsky made 29 saves.
Kevin Hayes scored a short-handed goal while Mika Zibanejad and Chris Kreider scored power-play goals for the Rangers.
Henrik Lundqvist made 26 saves. Lundqvist also withstood a collision with Columbus left winger Matt Calvert in the third period and stayed in the game after his shoulder hit the ice.
The Blue Jackets struck first with 6:06 remaining in the first period by winning a faceoff and executing effective puck movement.
Boone Jenner won a faceoff against Hayes and dumped the puck in behind the net where Thomas Vanek retrieved it. Vanek made a backhand pass and it appeared to surprise Wennberg, who hesitated before releasing a wrist shot from the slot that went over Lundqvist's glove side.
The Blue Jackets took a 2-0 lead with 10:32 remaining in the second when Panarin scored his first goal.
After Lundqvist stopped Calvert's wrist shot, the Blue Jackets retained possession and Ian Cole made a cross-ice pass through the slot. Panarin completed the play with a wrist shot over Lundqvist's glove side from the right circle.
New York scored with 6:16 remaining in the second after Jesper Fast broke up Wennberg's pass from behind the net. After creating the turnover, Fast connected with Hayes, who finished off a breakaway.
Nutivarra scored 4:05 into the third by finishing off Panarin's pass but the Rangers cut the deficit to one goal a little over three minutes later when Zibanejad's drive from the right circle went over Bobrovsky's right arm.
A little over four minutes later, Columbus regained a two-goal lead.
Lundqvist stopped Cam Atkinson's breakaway but was out of the crease and did not cover up the puck. Panarin pounced on the rebound and lifted a backhander into the net before Lundqvist could return to the crease.
New York scored its second power-play goal when Kreider redirected a shot by Brady Skjei with just under two minutes remaining but Panarin scored into an empty net with two seconds left.
--Field Level Media
Columbus | NY Rangers | |
Artemi Panarin 4 | Points | Kevin Hayes 1 |
Artemi Panarin 3 | Goals | Kevin Hayes 1 |
Ian Cole 2 | Assists | Pavel Buchnevich 1 |
N/A | Power Play Goals | Chris Kreider 1 |
N/A | Short Handed Goals | Kevin Hayes 1 |
Sergei Bobrovsky .906 | Save Percentage | Henrik Lundqvist .867 |
Sergei Bobrovsky 29 | Saves | Henrik Lundqvist 26 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Columbus | 31 | 5 | 0-2 | 2-4 | 8 | 31 |
NY Rangers | 32 | 3 | 2-4 | 2-2 | 4 | 25 |