Winnipeg jumped ahead 2-0 with a pair of goals 56 seconds apart in the second period, but the Rangers cut the deficit in half on Del Zotto's goal at 7:44 and changed the momentum.
"The entire building felt it," winning goalie Henrik Lundqvist said. "We started to get our game going. It was a big turning point."
Brian Boyle and Derek Stepan also scored, and Marian Gaborik added a pair of assists for the Rangers (49-21-7), who lead Pittsburgh by five points in the East. New York is tied with Western Conference-leading St. Louis with 105 points, but the Rangers have the edge because of one more non-shootout victory.
"Making it 2-1 instead of going down 3-0 was a key part of the game," Rangers coach John Tortorella said. "The last 35 minutes of the game is the best we've played in a while. Once we got our legs going and got away from a lack of discipline and killing penalties I thought we played really well."
Spencer Machacek and Bryan Little scored for the Jets (35-34-9), who are 10th in the East with 76 points. Winnipeg went 0-4 against New York this season.
Buffalo is currently eighth in the East with 84 points, followed by Washington, which is two points behind.
"It's difficult, for sure," Jets forward Tanner Glass said. "You play all year to get toward the playoffs, and when you kind of squander some chances at home here, that we feel were games we needed to win to get in, it's difficult.
"But I don't know if we're out of it yet, but we can't play like we are."
Lundqvist made 22 saves for the Rangers, who swept a two-game trip after a win at Minnesota on Tuesday. Ondrej Pavelec stopped 24 shots for Winnipeg.
New York's struggling power play connected for two goals.
"Our special teams need to be great in the playoffs for us to have success. It's something for us to build on," Callahan said. "We showed character. We have been doing it all year long."
The Jets have five games remaining, all against conference opponents. They will head out for a four-game road trip, starting at Carolina on Friday, and close out the regular season at home on April 7 against Tampa Bay.
Winnipeg is on its first three-game home losing streak of the season.
The Jets had all three power plays in a scoreless first period, including a two-man advantage for 1:44, and outshot the Rangers 11-4., but failed to score. They had another advantage 27 seconds into the second period on a boarding call against Boyle, but couldn't beat Lundqvist.
That changed soon after when Winnipeg connected for a pair of quick goals.
Machacek fired a shot between Lundqvist's pads at 3:58 and Little redirected a pass 56 seconds later for his 23rd goal of the season that made it 2-0.
The Rangers quickly responded with a short-handed goal and a power-play tally.
With New York center Brandon Dubinsky in the box for slashing, Callahan took the puck behind the net, spun around and sent a pass to Del Zotto in the slot. The defenseman put a low shot under Pavelec.
"The turning point in the game really was the short-handed goal that we gave up because they didn't have a lot of life," Jets coach Claude Noel said.
While Jets forward Alex Burmistrov was off for holding, Callahan scored his 28th goal of the season at 18:23.
Winnipeg captain Andrew Ladd was assessed a double minor for high-sticking 30 seconds later, and New York opened the final period on the power play.
The Rangers had 15 shots in the second period, and the teams were even with 19 each through two periods.
Just after Ladd's penalty expired, Boyle scored the winning goal when he tucked the puck between the post and Pavelec's stick at 3:07 to make it 3-2. Stepan gave New York a two-goal edge during a power play at 10:06.
New York was 2 for 5 with the man advantage. Winnipeg was 0 for 5.
"Once we got into some sort of flow, as far as getting people onto the ice, I think that's when we felt a lot more comfortable," Tortorella said.
The Rangers shut out the Jets both times at home this season. ... The Rangers, who will host Montreal on Friday, are the only Eastern Conference team the Jets haven't beaten this season.
Copyright by STATS LLC and The Associated Press
Arena: MTS Centre Location: Winnipeg, Manitoba
Referees: Gord Dwyer, Brad Watson Linesmen: Ryan Galloway, Brad Kovachik
Attendance: 15,004 (100.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
No scoring this period
Spencer Machacek (2)
Assists: Ben Maxwell, Mark Stuart
Bryan Little (23)
Assists: Blake Wheeler, Andrew Ladd
Michael Del Zotto (8)
(Shorthanded) Assist: Ryan Callahan
Ryan Callahan (28)
(Power Play) Assists: Marian Gaborik, Michael Del Zotto
Brian Boyle (9)
Assists: Ruslan Fedotenko, Ryan McDonagh
Derek Stepan (17)
(Power Play) Assists: Marian Gaborik, Brad Richards