Calvin Pickard made 28 saves in his first start since Feb. 18 for the Coyotes, who were eliminated from playoff contention Thursday and lost eight of their final 11 games.
"I thought we started OK, but you could tell the emotion that was there the last couple of months was lacking a bit," Richardson said. "We tried to fight back, but it definitely was tough."
Galchenyuk scored a power-play goal on Arizona's first shot. His wrist shot from the slot went in off Hellebuyck's glove to give the Coyotes a 1-0 lead at 2:21 of the first period.
The Jets scored the next four goals.
"We stuck with it, stayed pretty even-keeled the whole game, in the locker room and the bench," Connor said. "We generated some good offense and were able to capitalize."
Scheifele tied it 1-1 with a one-timer off Connor's pass from behind the net at 15:18.
"They kind of took over in the second," Pickard said. "They were opportunistic and made some nice plays."
Trouba put Winnipeg up 2-1 at 2:35 of the second when he pushed in the rebound of Par Lindholm's wraparound.
"When we get everybody involved, we're able to play at a high speed, and that's when we're at our best," Wheeler said. "If we continue to buy into this, it's going to give us a chance to have some success in the playoffs."
Connor scored on the rebound of a Scheifele shot two seconds after a Jets power play ended to make it 3-1 at 10:05, and Ehlers scored with two seconds left on a power play to make it 4-1 at 15:21.
"They've got their thing going again," Winnipeg coach Paul Maurice said of the Connor-Scheifele-Wheeler line. "It's looking like they're more on the same page now. … There's some chemistry there."
Richardson scored to get the Coyotes to within 4-2 at 3:29 of the third. He and Galchenyuk finished tied for the Arizona lead with 19 goals.
Josh Archibald scored for the Coyotes at 14:50 of the third, but Maurice challenged for goaltender interference by Archibald, and the goal was overturned after video review.
Winnipeg would have finished first in the Central Division with a win and a loss by the Nashville Predators, but the Predators defeated the Chicago Blackhawks 5-2 earlier in the night.
The Jets reached the Western Conference Final last season before losing to the Vegas Golden Knights in five games.
"It's something you can't take for granted," Wheeler said of making the playoffs. "It's not easy to do in this league."
The Coyotes were in position to make the playoffs until the final week of the season after being all but out of contention following an 0-10-1 start in 2017-18.
"We were a couple of games away this year," Richardson said. "We made huge strides, and we'd like to continue that next year."
