Jaromir Jagr added an empty-netter with 1.3 seconds left.
The Flyers beat the Devils 1-0 on Saturday in New Jersey. Henrique's first-period goal would have been enough to stand in this one. Brodeur was never seriously challenged against the NHL's weakest offense and posted his 122nd career shutout.
The Flyers have scored two goals in their last four games and have twice been shutout over that span.
The anemic Devils haven't been much better. They were blanked in their last two games, snapping the scoreless drought on Henrique's goal only 1:57 into the game.
Janssen scored in the third period.
Both teams lived up to their billing as the worst offenses in the NHL. The Devils entered next-to-last in the league with 27 goals while the Flyers were at the bottom with 22.
For as punchless as the Flyers offense has been, they were 52.3 seconds away from consecutive 1-0 wins after beating the Devils and holding a late lead against Carolina on Tuesday night. But the Hurricanes tied it in the final minute and won the game in overtime.
The victory did make it another big night at the Wells Fargo Center for New Jersey owners Joshua Harris and David Blitzer. They bought the Devils in August, giving them duel ownership with the NBA's Philadelphia 76ers. The rebuilding Sixers stunned Miami and Chicago in the building last week.
The Devils scored first when Eric Gelinas' shot was deflected from the high slot by Henrique past Ray Emery.
Emery got the start after the 1-0 shutout win over the Devils on Saturday. He stopped 14 shots in the win and 22 on Thursday.
Janssen redirected Adam Larsson's shot early in the third for the 2-0 lead.
The Flyers' offense put almost no pressure on Brodeur, taking just six shots in the second period. He scored just his fourth NHL goal in 313 games.
Flyers center Claude Giroux has not scored a goal in 15 games this season. He's twice scored 25-plus goals and averaged a point-per-game in last year's lockout-shortened season.
But he was just another Flyer booed off the ice between each period.
NOTES: Flyers F Steve Downie (concussion) did not play. ... Brodeur has 47 wins and 12 shutouts against the Flyers. ... The Flyers have lost seven of nine home games this season. ... The Devils won for the second time in 10 road games.