Scheifele tied the game 1-1 on a redirection of a Connor centering pass at 7:33.
"Our game got better as the game went on," Scheifele said. "We knew they were going to push, and they pushed all night. They played solid, they made us work for every inch."
Jets forward Brandon Tanev had a breakaway 9:14 into the second period but his backhand clipped the crossbar and went over the net.
The Blues had a chance to win the game late in the third period when Mathieu Perreault was called for tripping with 3:41 remaining but could not convert. The Blues were credited with one shot on the power play.
"I liked our penalty kill, a little bit like our 5-on-5 game ... when we have an opportunity to be aggressive we're picking the right time to do that, and when not, we're patient," Jets coach Paul Maurice said. "We're keeping our lanes covered pretty well."