The Giants showed off their sparkling new Skoda Stadium home and again demonstrated their competitiveness and promise for the future, but the Bombers took off in the third term en route to a 18.11 (119) to 7.11 (53) win.
It improves Essendon to 8-1, its best start to a season since 2001, while GWS remains on one win during its first year in the AFL.
Stewart Crameri, Alwyn Davey and Tom Bellchambers kicked three goals apiece for the visitors, while David Zaharakis, Jobe Watson and Nathan Lovett-Murray found plenty of the football.
Adam Treloar, Dom Tyson, Devon Smith and Dylan Shiel held their own for the Giants, with Jeremy Cameron kicking three goals in front of a modest crowd of 11,887.
Speaking on radio before the match, injured Giant Setanta O'hAilpin said the club was desperate to put in a committed effort for Sheedy, coaching for the first time against the side he led to four flags over 27 years.
""The boys want to put on a great show for him,"" O'hAilpin said. ""He deserves that. This is our mini Grand Final.""
And the young side responded early on, with only some wayward goal kicking preventing it from truly challenging the high-flying Bombers in the first half.
But 10 goals to five after the main break told a telling tale for the visitors.
It took less than one minute for the first goal to come at the AFL's newest stadium, via Essendon's Paddy Ryder.
Davey then had the visitors' second on the board three minutes later in an ominous start, but the Giants responded impressively, pinning the ball in their forward half for much of the next 20 minutes.
GWS had four shots on goal, but all were from outside 50m and all sailed wide before Smith's late miss from 40m on an angle gave them five behinds for the first quarter.
The Giants were queuing up to make history, but their excitement appeared to get the better of them as they continued to spray a succession of goal-scoring opportunities as the crowd's impatience increased.
The moment finally came at the 19-minute mark, with Shiel swooping on a loose ball and running into an open goal to release the intense pressure building up among the home fans.
At halftime GWS had managed 11 scoring shots to nine, but only returned 2.9 to Essendon's impressive 8.1.
It was then little surprise the floodgates opened after the main break as the Bombers flexed their muscles and the Giants received some more valuable AFL education.
Greater Western Sydney 0.5 2.9 4.11 7.11 (53)
Essendon 3.1 8.1 13.8 18.11 (119)
GOALS
Greater Western Sydney: Cameron 3, Shiel, Treloar, Giles, McDonald
Essendon: Crameri 3, Davey 3, Bellchambers 3, Ryder 2, Monfries 2, Zaharakis, Watson, Melksham, Hurley, Colyer
BEST
Greater Western Sydney: Treloar, Tyson, Kennedy, Cameron, Power, Shiel
Essendon: Dyson, Crameri, Lovett-Murray, Dempsey, Zaharakis, Davey
INJURIES
Greater Western Sydney: Folau (hamstring) replaced in selected side by Townsend
Essendon: Hardingham (calf) replaced in selected side by Slattery
SUBSTITUTES
Greater Western Sydney: Sam Darley replaced Adam Kennedy at three-quarter time
Essendon: Henry Slattery replaced Ricky Dyson at three-quarter time
Reports: Nil
Umpires: McBurney, Ryan, Hosking
Official crowd: 11,887 at Skoda Stadium
