Tomas Tatar had a goal and an assist, and Carey Price made 30 saves in his 11th straight start for Montreal (29-28-9), which is 2-5-2 in the past nine games.
"I don't know what else to say, we can't blow it like that," Tatar said. "We had 40 great minutes and we were really happy about our hockey game, and then we just dropped it. And I don't think they played any better. We were worried to close the game, but something's got to change. We've got to look at ourselves in the mirror and we can't let it happen."
Montreal is nine points behind Columbus, and nine behind the Toronto Maple Leafs for third place in the Atlantic Division.
Zibanejad equaled his NHL career high he set last season with his 30th goal to tie it 2-2 at 11:06 of the third period. Rangers coach David Quinn changed his lines in the second, putting Artemi Panarin with Zibanejad.
"He does such a good job with kind of keeping the puck and keeping the defensemen guessing there and creates enough room for me to get away that shot," Zibanejad said of Panarin. "He's incredible with the puck and his hockey IQ is through the roof, obviously, and you've seen that throughout the whole season. It was an unbelievable play and I'm lucky that it went in and tied the game, and I thought we changed it after that."
Adam Fox made it 3-2 at 12:21. Strome extended the lead to 4-2 at 15:23 on a power play and scored into an empty net at 18:27 for the 5-2 final.
"I thought we played a very good 40 minutes, then just shelled up in the third, and again that didn't work for us," Price said.
Max Domi put Montreal up 1-0 when his pass went in off Fox's left skate at 3:12 of the first period. Tatar scored on a breakaway at 17:01 of the second to make it 2-0.