Elvis Merzlikins made 33 saves for the Blue Jackets (4-3-0), who are 0-2-0 on the road.
"Too many mental mistakes," Blue Jackets coach Brad Larsen said. "I liked our first six, seven minutes and then just blowing coverages. We talked about it, we had to skate. We stopped skating. We gave up way too much and it just snowballed the wrong way for us.
"It wasn't good enough."
The Blue Jackets had five shots on goal through the first 2:28 of the first period, but they couldn't take advantage and eventually the Rangers forecheck and speed through the neutral zone started to get the best of them.
Ryan Strome scored his first goal of the season to for a 1-0 lead at 12:29 of the first period.
Panarin carried the puck across the blue line and pulled up to wait for Strome, who was skating in as the trailer. He found him and Strome, with his momentum going forward, beat Merzlikins with a glove-side wrist shot from high between the circles.
"We kind of lose ourselves once they scored their first goal," Blue Jackets defenseman Zach Werenski said. "It kind of took the life out of us, for whatever reason, and we just couldn't find our game after that. There were shifts where we did some good things, shifts where we had chances, but for the most part it wasn't to a standard we know we can play at."
Alexis Lafreniere, the recipient of a terrific cross-slot pass from Fox, scored his third goal 3:02 later with a one-timer from the right circle to make it 2-0.
Fox carried the puck behind the goal line and curled around the net. He looked up as he got around the left post and saw a passing lane to Lafreniere, who was coming down the right circle. He delivered a pass through the high-traffic area onto Lafreniere's tape for the one-timer.
"I just turned and looked, and I was looking at the other side and then saw him on the backside," Fox said. "Nice shot by him to put that in."