It was the second straight win for the Jets against the Senators. They end the three-game set Saturday at Winnipeg.
"You've got to move fast and move the puck quickly; we had lots of support there, lots of conversation on the ice, lots of communication, guys calling for pucks," Jets coach Paul Maurice said. "And then we got off to a pretty good run of going from our end to their end."
Ehlers' wrist shot from the top of the slot gave the Jets a 1-0 lead at 11:50 of the first period.
"Those ones just can't go in," Murray said. "There's no excuse for that."
Scheifele tapped in a pass from Connor at the side of the net to make it 2-0 at 4:22 of the second, and Adam Lowry scored into an open net at 7:05 for a 3-0 lead.
"He's the guy who gets different wingers all the time. [He's] a guy who scored 15 in this league (in 2016-17)," Maurice said of Lowry. "We think it's there. It's the face-off goal the other night where he goes to the goal and gets a tip on it. Big man driving the net. Some of it is confidence, some of it is rhythm. With our injuries he's getting some power-play time, he's getting the [penalty-kill] time, he's playing a big-minute game for us, so he's in that rhythm, he feels good."
Blake Wheeler took a seam pass from Scheifele and finished a backhand deke at 13:55 to increase the lead to 4-0.
Tierney redirected a cross-ice pass from Nikita Zaitsev to make it 4-1 at 17:03 of the third.
"We had some competitive guys, but we had a lot of guys that couldn't match their level of speed and competitiveness," Smith said. "That's not acceptable."
NOTES: Jets forward Nate Thompson left in the first period with a lower-body injury. There was no update. … Hellebuyck is 150-86-22 in six seasons with Winnipeg. … The Jets were 0-for-7 on the power play. … Jets defenseman Ville Heinola was plus-2 in 14:22 in his season debut. … Connor (three goals, four assists) has the second-most points through four games in Jets/Atlanta Thrashers history. Marc Savard had eight (two goals, six assists) in 2005-06. … Zaitsev had an assist, his fifth in four games. He had 11 in 58 games last season. ... Ottawa outhit Winnipeg, 51-14. Defenseman Erik Gudbranson led the Senators with six.