Jets defenceman Dylan Samberg attempted to clear the puck off his end boards but hit forechecking Vegas forward Ivan Barbashev's right leg and ended up right on Amadio's stick in the high slot.
The Vegas winger simply fired the puck past a tired Connor Hellebuyck, beating him with a high shot to give the Golden Knights the win.
Adam Lowry managed to get the game to overtime, scoring the tying goal with just 22 seconds left in regulation.
The Jets scored three times in the third period to force overtime after being outscored and outshot in the game's first two stanzas.
Pierre-Luc Dubois nearly ended the contest 9:35 into the first overtime but hit the goal post.
Jack Eichel scored twice and added an assist to pace the Vegas Golden Knights in scoring.
Eichel, who was largely ineffective in game one of the series, has improved steadily, scoring once in game two before game three as he had three-point outing.
Connor Stephenson had a goal and an assist for the Golden Knights.
Keegan Kolesar also scored for Vegas.
Alex Pietrangelo had a pair of assists.
Lauren Brossoit turned aside 30 shots to pick up the win for the Golden Knights.
Kyle Connor had a goal and an assist for the Jets.
Nino Niederreiter and Mark Scheifele also scored for Winnipeg.
Neal Pionk added a pair of assists.
Connor Hellebuyck made 43 saves for the Jets, who lost their second straight series game.
The game got off to a physical start with Vegas forward Keegan Kolesar and Winnipeg defenceman Brendan Dillon dropping the gloves 49 seconds into the contest.
Connor Stephenson got Vegas the lead 2:52 into the first when he broke in on Hellebuyck on a two-on-one with Mark Stone before snapping a high wrister past him to make it 1-0 Golden Knights.
The goal was his 2nd of the playoffs.
Jack Eichel gave Vegas a two-goal cushion with a power play markerat 6:18 when Chandler Stephenson found him alone in the right face-off circle and hit him with a cross ice pass which he promptly one timed past Hellebuyck, beating him low blocker side just inside the left post.
The goal was his 2nd of the playoffs.
Winnipeg had been a perfect 7-for-7 on the penalty kill until Eichel's goal.
Kyle Connor cut the Vegas lead in half at 9:07 when he deflected a Dylan DeMelo shot past Brossoit from the high slot to make it 2-1.
The goal was his 2nd of the playoffs.
Winnipeg nearly tied it 4:45 into the second when Brendan Dillon's shot from the left point hit the inside of the post.
With Dylan Samberg off for tripping Vegas took the lead 10:49 into the second on the power play when Alex Pietrangelo found Jack Eichel and the Vegas winger hammered the disc through Hellebuyck's pads to make it 3-1.
The goal was his 3rd of the playoffs.
Keegan Kolesar gave Vegas a three-goal lead 17:45 when he pounced on a rebound off a Jack Eichel slap shot and backhanded it past Hellebuyck to make it 4-1.
The goal was his first of the playoffs.
Nino Niederreiter pulled the Jets to within a pair of goals just over two minutes into the third period.
Niederreiter had control of the puck in the neutral zone before working a give-and-go with Pierre-Luc Dubois just inside the blue line as the Jet forward snapped a high shot past Brossoit, beating him glove side to make it 4-2.
The goal was his first of the playoffs.
Mark Scheifele scored on the power play at 14:08.
With Phil Kessel off for holding-the-stick, Neal Pionk found Scheifele alone near the top of the faceoff circle.
Scheifele moved in a notch before unleashing a high wrister, beating Brossoit glove side to make it 4-3.
The goal was his first of the playoffs.
Adam Lowry tied the game with 21.9 seconds left in regulation to send the game to overtime after sending a rebound off a Neal Pionk shot past Brossoit to make it 4-4.
The goal was his 4th of the playoffs.
Vegas began overtime with a power play but were unable to score.,p> Pierre-Luc Dubois came close to ending the contest when he hit a goal post at 9:35 of overtime.
There was no scoring in the first overtime.
The two teams face each other Monday night as Winnipeg hosts game 4.
SHOTS-VEGAS 48 WINNIPEG 34
ATTENDANCE-15,324
