Essendon kicked six of the last seven goals to consign West Coast to its fifth home loss of the season, 15.8 (98) to 13.13 (91).
Watson was Essendon's hero on a night where West Coast fans booed him like a pantomime villain.
"I did not like that at all," Essendon coach James Hird said.
"It wasn't necessary … I just don't think it was called for."
Five talking points: West Coast v Essendon
Every one of Watson 29 touches were accompanied by jeers, but his two second-half goals inspired his teammates above and beyond.
"Jobe, he is incredible" Hird said.
"To play the way he did under the pressure he was under was just outstanding," Hird said.
The Bombers trailed by 17 points at three-quarter time but goals to Watson, Alwyn Davey and Brendon Goddard saw Essendon hit the front.
Mark LeCras' third goal reclaimed the lead for West Coast but Jake Carlisle's second major from a set shot on the boundary levelled the scores once more.
A key touch from Watson led to a Jake Melksham behind to tip the game in Essendon's favour in the dying minutes. Dyson Heppell sealed it with seconds left to give the Bombers another famous win in Perth after their heart-stopper against Fremantle in round three.
Click here to vote for the three best Essendon players from the game
The Eagles were able to lift their pressure and intensity to control the match through the first three quarters. The infamous West Coast press that has been absent for large parts of the year was employed with great effect to trap the ball in their forward half.
"You couldn’t ask any more from their effort, I don’t think. I was really rapt with the way the guys went about it," Eagles coach John Worsfold said.
Both sides traded goals in differing styles in the opening half. West Coast continued to pressure every Bomber possession in the back half but could not make the most of their chances to establish a lead.
Essendon likewise were able to break through the press on a couple of occasions but some skill errors meant the Bombers couldn't hurt West Coast on the scoreboard, as the Eagles led by three points at half time.
West Coast took the ascendency in the third term courtesy of Matt Priddis. His clearance work gave the Eagles plenty of drive and he finished with 32 disposals and a goal.
Jack Darling kicked three goals in a powerful display up forward.
Click here to vote for the three best West Coast players from the game
But yet again they were unable to put the game away. For the third time this season they lost after outscoring their opponents. The Eagles finishing has hurt them all year and their finals aspirations have taken a decisive blow although Worsfold still believes in his group.
"I think we could win every other game this year. That's our aim," Worsfold said.
The Eagles injury crisis deepened after Luke Shuey was a late withdrawal with a hamstring injury.
"He hurt his hamstring on Wednesday at training, so we would expect that he will miss another week, but we will wait and see," Worsfold said.
Below: Jobe Watson celebrates an emotional win with coach James Hird. Picture: AFL Media
WEST COAST 3.4 6.6 12.10 13.13 (91)
ESSENDON 4.1 6.3 10.5 15.8 (98)
GOALS
West Coast: Darling 3, LeCras 3, Dalziell 2, Kennedy 2, Kerr, Priddis, Cox.
Essendon: Winderlich 3, Watson 2, Carlisle 2, Davey 2, Merrett, Ryder, Dempsey, Crameri , Goddard, Heppell.
BEST
West Coast: Priddis, Cox, Darling, Dalzeill, Masten, Glass, Gaff.
Essendon: Watson, Carlisle, Ryder, Winderlich, Dempsey, Melksham, Hooker.
INJURIES
West Coast: Shuey (hamstring) replaced in selected side by Schofield.
Essendon: Crameri (ankle).
SUBSTITUTES
West Coast: Simon Tunbridge replaced Brad Sheppard in last quarter
Essendon: David Myers replaced Tom Bellchambers in third quarter.
Reports: Nil
Umpires: Margetts, Kamolins, Chamberlain
Official crowd: 36,451at Patersons Stadium
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