Wheeler drove the slot, held off Nino Nieddereiter after a pass from Patrik Laine, and scored to make it 2-0 at 5:48.
A strong Jets forecheck resulted in a 3-0 lead. Kyle Connor's pass from the right corner connected with Ben Chiarot, who scored from the slot at 9:16.
Hayes sent a backhand from along the end boards to Ehlers between the face-off circles for a one-timer to make it 4-0 at 18:44.
"[Ehlers] is a great player, him and Kyle Connor," Hayes said. "They're both elite players in this league and easy and fun to play with. Tonight, we played pretty well."
Winnipeg coach Paul Maurice sees chemistry developing between Hayes and his linemates.
"For [Hayes], he's a real smart positional player, and he's got a good set of hands," he said. "Having [Ehlers and Connor], who are as fast as there are in the League, can open up some room. Both those guys like to shoot the puck, Kevin likes to pass it, so it looks like it's got something going."