Hart (21 years, 57 days) is the youngest Flyers goalie with a shutout; Dominic Roussel was 22 years, 5 days old when he shut out the Calgary Flames on Feb. 27, 1992.
"Anytime you have a milestone, it is definitely pretty cool," Hart said. "But I think it's huge that we came out so hard in our home opener. The fans were really getting into it. We gave them something to cheer about, so I think that was a huge effort by us tonight to come out so hard."
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Ivan Provorov and Travis Konecny each had a goal and an assist for Philadelphia, which won its first game in North America after a 4-3 victory against the Chicago Blackhawks on Friday in the 2019 NHL Global Series at O2 Arena in Prague, Czech Republic.
Kevin Hayes and Sean Couturier also scored for the Flyers.
Cory Schneider made 30 saves for New Jersey, which has lost three straight to start the season (0-2-1).
"I thought the first was a good period for us," Devils coach John Hynes said. "Second period, we didn't get out of our own end enough. We got hemmed in with some execution things, weren't able to get in the offensive zone and have some pressure like we had in the first period. Then special teams were a factor tonight."
Philadelphia scored two power-play goals and allowed four shots on five New Jersey power plays, which included two 5-on-3 advantages.