With a shutout, Fleury joined Martin Brodeur and Patrick Roy as the only NHL goaltenders to reach 500 career victories.
As the clock reached zero, Blackhawks teammates rushed over to Fleury in celebration.
Jonathan Toews and Henrik Borgstrom scored for Chicago. Patrick Kane and Seth Jones picked up assists.
Jake Allen had 23 saves for Montreal.
Kane had the opening goal on the tip in the final moments of the first period, intercepting Allen’s clearing try and scoring into an open net.
Toews scored at 13:48 of the second period on the power play. It was the Blackhawks captain’s first goal since the 2020 NHL playoffs in the Edmonton bubble.
Borgstrom added Chicago’s insurance goal 12 minute into the third period. He intercepted Alexander Romanov’s pass in front of Allen’s net and easily tapped his second goal of the season.
NOTES: The Canadiens broke a franchise record for most games in a calendar year, having played 106 regular-season and playoff games in 2021.
Blackhawks: At Toronto Maple Leafs on Saturday.
Canadiens: At St. Louis Blues on Saturday.