Ian Laperriere, Darroll Powe and Matt Carle also scored as the Flyers made Devils goalie Martin Brodeur look very ordinary in his 1,000th career game.
Brodeur, the NHL's winningest goaltender, is 30 games shy of surpassing Patrick Roy for most games by a netminder.
Emery, who signed with the Flyers as a free agent after playing a season in Russia, was by far the better goaltender in the season opener for New Jersey.
Brodeur played so poorly that the crowd derisively cheered after he made a couple of saves in the second and third periods.
After stopping 28 shots in blanking the Carolina Hurricanes 2-0 on Friday night, Emery put on a show against New Jersey. He stopped Jay Pandolfo and Travis Zajac point blank in the first period as the Flyers withstood two two-man disadvantages.
Emery also stopped Zajac in close early in the second period on a power play and he made a diving glove save on Pandolfo after losing his stick in a melee in front.
Carter gave the Flyers the lead for good with 4:03 left in the first period. He skated into the left circle after taking a pass off the boards from Scott Hartnell and tried to center the puck. The pass hit off defenseman Johnny Oduya and went back to Carter, who then wristed a shot past Brodeur.
Laperriere stretched the lead to 2-0 midway through the second period with a shot from the right circle that hit off Brodeur's shoulder and went into the net.
Richards came out from behind the net and stuffed a shot past Brodeur with the puck hitting the goaltender's stick and bouncing up and into the net.
Powe and Carle scored on shots from the left circle that either hit off Brodeur's glove or went under his arm.
Rolston ended Emery's shutout streak with a blast from between the circles while Jamie Langenbrunner closed out the scoring with a short-handed goal.
NOTES: Devils F Patrik Elias is expected to be sidelined another 3-4 weeks following groin surgery. ... Flyers rookie LW James van Riemsdyk has three assists in his first two games. ... This marked the first time in Flyers' history that they have opened the season with consecutive road wins.