Eichel took a cross ice feed from Mark Stone and promptly snapped the disc over a sagging Laurent Brossoit's left shoulder to give the Golden Knights their fifth straight win to start the NHL season.
Jonathan Marchessault, Brett Howden and Alec Martinez also scored for Vegas, who won their 5th game of the season.
Shea Theodore had three assists.
Mark Stone had a pair of assists.
Logan Thompson turned aside 35 shots for the Golden Knights (5-0-0).
Alex Iafallo netted two goals for Winnipeg.
Cole Perfetti scored the other Jet marker.
Nikolaj Ehlers had two assists.
Laurent Brossoit made 22 saves for the Winnipeg, lost their second straight game to drop to 1-3-0.
Alex Iafallo got Winnipeg on the board 1:30 into the contest when he drove the net and snagged the rebound off a Josh Morrissey shot, snapping the disc past Logan Thompson to give the Jets a 1-0 lead.
Kyle Connor nearly made it 2-0 at 11:32 when he grazed the post off the rush but Vegas cleared the puck out of the zone.
Jonathan Marchessault evened the contest at 17:42 on the power play when he one timed a Chandler Stephenson feed from the side boards past Brossoit from the high slot.
The goal was his 2nd of the season.
Brett Howden scored 49 seconds into the second to give Vegas the lead after he finished off a two-on-one pass from Mark Stone to score his first of the season.
Alec Martinez gave the Golden Knights a two-goal cushion 15:27 into the second when he canned a William Karlsson feed from the corner past Brossoit as he snapped a wrister off the goal post.
Cole Perfetti replied 33 seconds later when he finished off a three-way passing play off the rush with a backhand deke after Vladisav Namestnikov sent him in alone at 16:00.
The goal was his 1st of the season.
Alex Iafallo netted his second of the contest on the power play at 11:32 of the third period.
With Ivan Barbashev off for holding, Nikolaj Ehlers and Mark Scheifele worked the puck in close to the net before Scheifele left a backhand drop pass for Iafallo who snapped the disc past Thompson to knot the score at 3.
The goal was his third of the season.
Jack Eichel scored on the power play with 4:36 remaining in regulation to give Vegas the lead as the picked the top corner blocker side on Brossoit after Mark Stone hit him with a cross slot feed.
Nicolas Roy added an empty netter with just over a minute left in regulation to seal the win for the Golden Knights.
SHOTS-LAS VEGAS 26 WINNIPEG 38