The Rangers captain moved back and forth behind the New Jersey net and shifted the puck from backhand to forehand before throwing the puck out front to the waiting Stepan, who unleashed a lightning-fast one-timer that beat Hedberg just 2:37 in for his 18th goal.
The pair teamed up again in the final minute of the period while Taylor Pyatt served a questionable hooking penalty. Stepan intercepted the puck from defenseman Marek Zidlicky and send a lead pass ahead to Callahan for the short-handed breakaway.
Callahan darted from side to side as he raced in on Hedberg, and deked enough to open up the goalie's pads to slip the puck in with 58.8 seconds left in the period.
It was Callahan's 16th goal of the season.
"It's been fun so far," Stepan said of playing with Callahan and Carl Hagelin. "Those two guys just work so hard, and when they get on pucks it's hard to get it off their stick."
Just over 6 minutes in, while Hagelin was off for tripping, Callahan had another short-handed chance when he got past Ilya Kovalchuk in the New Jersey zone and came in alone on Hedberg, but he was denied at the right post.
The Rangers looked much better while killing penalties than on their one power-play chance in the first. After taking a 7-1 lead in shots early in the period, New York finished with only a 9-8 edge.
Nash garnered the Rangers' third short-handed break of the game with 6:55 left in the second, but his rush was thwarted by the back-checking Kovalchuk, who got his stick in on Nash's hands — forcing the Rangers forward to his knees and having him push the puck wide of the net.
Nash would connect with 2:37 remaining after the Rangers won a faceoff in the New Jersey end. Brad Richards sent a pass from behind the net out to Nash, who snapped off a wrist shot from the edge of the left circle for his 20th goal of the season.
Nash made it 4-0 at 5:30 of the third when he whipped a shot from the slot past Hedberg off a feed from Mats Zuccarello.
The chants of "We Want Marty" started after Callahan's goal and grew even louder after Nash made it 2-0. The nearly 41-year-old Brodeur watched his team's final game of the season from the bench.
It was the first time the longtime Devils No. 1 goalie served as the backup for a game at Madison Square Garden since May 1, 1992, in Game 7 of a first-round playoff series against the Rangers, according to the Elias Sports Bureau.
NOTES: Nash reached 20 goals for the ninth straight season. ... Richards has a six-game point streak (five goals, six assists). ... The Devils finished 19-19-10 and 6-10-8 on the road. ... Rangers LW Ryane Clowe sat out after being injured on Thursday. He was replaced by Kris Newbury, recalled from the AHL on Friday.