Connor Hellebuyck made 14 saves for the Jets (10-8-4), who have lost six of their past seven games (1-5-1).
"When you go through tough times, that's when you find out what you're made of," Winnipeg captain Blake Wheeler said. "If you just coast through the season and score goals at will, you're going to get punched in the mouth in the playoffs. How are you going to deal with it? I think our group going through some adversity and learning how to win games without relying on the offense, that is going to make us grow a lot."
Roussel made it 1-0 at 17:59 of the second period. He redirected Loui Eriksson's backhand centering pass at the top of the crease after Nikolaj Ehlers turned the puck over in the neutral zone.
"I'm really proud of our group," Coyotes forward Christian Fischer said. "Gosh that felt good. That was a grind, a mucky win. [Vejmelka], obviously, all credit goes to him. What a performance, and well deserved."
Winnipeg outshot Arizona 14-3 in the third period and had a four-minute power play with 5:08 remaining, but couldn't tie the game.
"I don't think our best chances may have hit the net," Jets coach Paul Maurice said. "We had some really good ones that we missed out on, and we've got to get a little heavier net front. Those are the basics of your offensive game. But you get into those situations where you've got the puck and it's traffic and there's not an easy place to put it [on net]. You keep it to the outside more. But it's net front that will be the place that things will start going for you."
NOTES: Fischer, who was removed off injured reserve earlier in the day, had two shots and two hits in 16:49 of ice time after missing the past seven games with an upper-body injury. … Roussel has scored in consecutive games for the first time since Dec. 3-7, 2019. … The Jets were 0-for-6 on the power play and are 2-for-34 in their past 12 games.