Scheifele put the Jets back in front 39 seconds into the second period on a one-timer off a cross-seam pass from Blake Wheeler to make it 2-1.
Sheahan tied it 2-2 at 4:39. His initial shot in the slot was saved by Hellebuyck, but the puck dropped in behind the Jets goaltender and Sheahan was able to push it across the line.
Scheifele's second goal of the game gave the Jets a 3-2 lead at 16:00 of the second period when his wrist shot beat DeSmith for his 13th goal of the season.
"We've just go to play the way we know how to," Scheifele said of protecting third-period leads. "We get away from it, we start doing things that aren't part of our strategy. We turn pucks over, we don't get pucks deep. We've just got to simplify in those areas.
"We're a simple team, we get it deep, we work teams in the offensive zone and make them go an extra 30 to 50 feet every time. You turn it over, they're going to make you pay."