Hunt tied it 1-1 at 3:55 of the third period, stopping Vincent Trocheck's cross-crease pass with his skate before scoring high glove side.
"When you get an opportunity like that, especially with coming into the lineup, you kind of want to make the most of it," said Hunt, who was playing in his second game of the season. "[Hellebuyck] was pretty good all night, so for that one to go in was huge. It just would have been nice to kind of keep it rolling, I guess."
Gagner, who signed a one-year contract Sept. 2, put Winnipeg in front 2-1 at 15:35 when he knocked in his own rebound.
"It feels great," Gagner said of the standing ovation he received after scoring. "The fan support here is incredible. I've only been here for a short time, but you can see the passion from the fanbase, and everyone's been really welcoming, from my teammates to the fans. It's been great so far, and hopefully keep it rolling."
Scheifele pushed the lead to 3-1 with a power-play goal from the bottom of the left face-off circle at 18:23, and Connor scored into an empty net at 19:40 for the 4-1 final.
"Outside of that first and that third, I think we know what works for us," New York captain Jacob Trouba said. "We just got away from it a little bit tonight. We're not going to play perfectly every game this year, so we'll learn from it and address it going forward."
NOTES:Rangers forward Ryan Carpenter left the game in the second period because of an upper-body injury. Gallant said he is day to day. … New York forward Artemi Panarin had an assist and has six points (one goal, five assists) in a three-game point streak. … Trouba played his 600th NHL game. The defenseman played his first 408 games with the Jets before signing a seven-year contract with the Rangers on July 19, 2019.