Fleury overtook Tom Barrasso for the record while Beau Bennett, Pascal Dupuis and Tyler Kennedy scored the goals as the Penguins stretched their winning run to eight.
Dustin Jeffrey contributed two assists.
Two goals apiece from Jonathan Toews and Marian Hossa helped the Chicago Blackhawks to an 8-1 win over the Dallas Stars.
Nick Leddy and Patrick Kane each had a goal and an assist, while Johnny Oduya and Duncan Keith also tallied.
Trevor Daley got the lone score for the Stars.
Kyle Turris scored two including an overtime winner as the Ottawa Senators edged out the Buffalo Sabres 4-3.
Patrick Wiercioch and Chris Phillips also scored for the Senators.
Devin Stoguchi scored twice to help the Minnesota Wild to a 6-4 win over the Colorado Avalanche.
Sergei Bobrovsky stopped 39 shots for the shutout and the Columbus Blue Jackets needed a shooutout to beat the Phoenix Coyotes 1-0.
Chris Stewart scored an overtime winner to see the St Louis Blues to a 2-1 triumph over the Anaheim Ducks.
The Detroit Red Wings and the Los Angeles Kings were both 5-2 winners, over the Vancouver Canucks and the San Jose Sharks respectively.
The Montreal Canadiens got their fifth straight win with a 2-1 victory over the New Jersey Devils, while the Winnipeg Jets were 5-4 victors over the Toronto Maple Leafs after a shootout.
The Boston Bruins were 4-1 winners over the Washington Capitals, the New York Islanders edged out the Florida Panthers 4-3 and the Tampa Bay Lightning saw off the Carolina Hurricanes 4-1.