Jaccob Slavin and Sebastian Aho scored in the third period for the Hurricanes (13-13-4), who are 1-4-1 in the past six games. Petr Mrazek made 34 saves.
"This is where I've got to be careful because I'm not happy and we needed much more out of certain guys and didn't have it tonight," Carolina coach Rod Brind'Amour said. "So that's frustrating, especially after we fight to get back. You know, a terrible game, we're playing terrible, and then we dig and get back and then make just really bad decisions. And that's the frustrating part for me."
Lehkonen gave Montreal a 4-2 lead at 4:22 of the third, and Slavin scored at 10:51 to make it 4-3.
Shaw extended his point streak to six games for a 5-3 lead at 12:24. Aho got Carolina within 5-4 at 15:38.