The Jets, who were the NHL's best home team last season, finishing with a 32-7-2 record at Bell MTS Place, held the Kings to just 17 shots on goal. Winnipeg advanced to the Western Conference finals last season, getting eliminated by the Vegas Golden Knights.
Ilya Kovalchuk scored a first-period goal for the Kings, who were playing their first game on the road after an overtime loss and a victory at Staples Center to open the season.
Kovalchuk, in his 12th NHL season but first with the Kings, scored his first goal with his new team. He played his first eight NHL seasons with the Atlanta Thrashers, leaving after the 2009-10 season. The Thrashers moved to Winnipeg for the start of the 2011-12 season. Kovalchuk spent the past five seasons in Russia.
The Kings were playing their second game without veteran goalie Jonathan Quick, who is considered week-to-week with a lower-body injury suffered in practice Saturday. Kings backup goalie Jack Campbell made 37 saves in his seventh career start.
After an elaborate pregame ceremony, the Kings got the early jump on the Jets with Kovalchuk's goal 6:26 into the game. He redirected a centring pass from Drew Doughty past Hellebuyck.
Doughty was playing in his 331st consecutive game for the Kings, passing Anze Kopitar's franchise record.
The Jets wasted little time getting even, with Scheifele scoring at the 10:59 mark of the opening period. Scheifele's first goal of the season came from point-blank range after a centring pass from Brandon Tanev.
The goal was Scheifele's first of the season and also his first career goal against the Kings. He has now scored against every NHL team.
Winnipeg went ahead for good in the second period when Connor scored a power-play goal at the 10:21 mark, his third goal of the season in three games. Connor's first shot off a pass from Blake Wheeler was saved by Campbell, but he poked the rebound back into the net.
The Jets had 33 shots on goal to the Kings' nine after two periods and had a 39-17 advantage for the game.
(With inputs from agencies.)