Brandon Tanev appeared to make it 4-1 at 15:40 of the second period. But Dallas coach Ken Hitchcock challenged, and the goal was overturned when it was ruled that Scheifele interfered with Bishop.
Janmark used Jets defenseman Jacob Trouba as a screen to make it 3-2 at 18:26, his third goal of the season.
Scheifele scored his second of the game at 1:47 of the third, tipping a shot over Bishop to make it 4-2.
"In this league, if you're down 3-0 in the first, it's hard to come back," Radulov said. "I think we did a pretty decent job in the second. Some moments, I think, we were on top of them with a chance to come back, but then [they got the fourth] and they kind of tried to play more defense and we tried to force things. It wasn't there today."
Jets forward Kyle Connor was awarded a penalty shot at 15:09 of the third but failed to get a shot on goal.
Scheifele completed the hat trick at 19:00, scoring into an empty net.