Bjugstad restored Florida's one-goal lead at 2-1 with 12.2 seconds remaining in the period.
McKegg scored his second goal on a backhand to increase the lead to 3-1 at 8:58 of the third, and Hudler scored a power-play goal at 18:31.
Panthers defenseman Brian Campbell was given the Panthers' coveted "Spacey in Space" hoodie by his teammates after playing his 1,000th NHL game. It was his 384th consecutive game, including 374 straight with Florida, breaking the Panthers record set by Olli Jokinen from Dec. 12, 2002 to April 5, 2008.
"They didn't have to do that, but it's nice for the guys to do that, and it's a great night, a great building to play [my 1,000th game] in too, so I'm a pretty lucky guy," Campbell said.
John Scott, the Most Valuable Player in the 2016 Honda NHL All-Star Game in Nashville, made his Canadiens debut and started at left wing. He lined up for the opening faceoff opposite Jagr.
"You never want to give up a goal on the first shift," Scott said. "You've just got to move on. You can't really dwell on it. I thought we bounced back, my line played pretty well and got some good chances. But yeah, it's not the ideal start we were looking for."