The Devils took a 1-0 lead just 1:32 in when Henrique beat Martin Biron with a backhander in front during a power play. But the advantage didn't last long as the Rangers struck for a pair of goals just over a minute apart.
Richards, in his first game with New York since signing a nine-year, $60 million deal, tied it at 4:22 when his centering pass intended for Wojtek Wolski was deflected in by New Jersey rookie defenseman Adam Larsson.
Stepan put the Rangers in front at 5:43 when he took a pass from Ruslan Fedotenko at the outer edge of the right circle and snapped a shot past Brodeur, who made his preseason debut.
"I felt pretty good out there," Brodeur said. "It was the first time in pads in a game situation for the first time in a long time, but I felt good. They rolled out three lines of NHL-ready players out there in a preseason game, and that's a lot for this time of year. But there's plenty to work on."
Gaborik, expected to be on Richards' right this season, made it 3-1 at 1:32 of the second period with a power-play goal. He also assisted on Richards' first-period goal. New York was successful in its experiment of using five forwards and no defensemen on the power play.
"The power play looked pretty good," Gaborik said. "We were moving the puck well. Five forwards ... so far, so good. Hopefully, we won't make any turnovers so we can keep it up there."
The Devils stormed back in the second on Josefson's goal at 7:26, and Kovalchuk's goal with 3:15 left in the period and 1 second remaining on New Jersey's two-man advantage.
Biron was replaced by Johnson at the start of the third period after stopping 13 of 16 shots. Henrik Lundqvist got the night off after playing against the Devils two nights earlier.
This was New York's second-to-last game in North America before the regular season begins. The Rangers will play at Philadelphia on Monday before heading to Europe for four exhibition games, beginning next week. New York will then face Los Angeles and Anaheim in season-opening games in Sweden.
Copyright by STATS LLC and The Associated Press
Arena: Prudential Center Location: Newark, New Jersey
Referees: Kelly Sutherland, Jean Hebert Linesmen: Jean Morin, Tim Nowak
Attendance: 14,719 (83.5% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Adam Henrique (1)
(Power Play) Assists: Ilya Kovalchuk, Adam Larsson
Brad Richards (1)
Assists: Marian Gaborik, Wojtek Wolski
Derek Stepan (1)
Assists: Ruslan Fedotenko, Brendan Bell
Marian Gaborik (1)
(Power Play) Assists: Ryan Callahan, Brad Richards
Jacob Josefson (1)
Assist: Ilya Kovalchuk
Ilya Kovalchuk (1)
(Power Play) Assists: Adam Larsson, Petr Sykora