Early on, it appeared Essendon could repeat last week's rout of the Western Bulldogs as they asserted their dominance early, dashing out to a 17-point quarter-time lead.
However, the Swans re-grouped in the following stanza, allowing more run and carry and entering the main break with much-needed momentum.
When Swans pair Jude Bolton and Josh Kennedy opened the second half with back-to-back goals the Swans were sudden two-point leaders and looking the more assured of the two sides before fading late to trail by 10 points at three-quarter time.
A shootout then ensued between the two sides in the final quarter, going goal-for-goal before Jude Bolton's goal with three minutes to go saw his side hit the front by five points, a lead they refused to relinquish until the final siren.
For Sydney, Bolton was instrumental in the win, standing up when required and finishing with 25 possessions and three goals while teammate Ryan O'Keefe led the disposals count, collecting 27 touches.
Essendon captain Jobe Watson continued his impressive start to the year with 24 disposals while youngster Dyson Heppell followed on from last week's NAB Rising Star nomination with 21 of his own.
Essendon had the better of the opening term thanks to back-up big man Tom Bellchambers and Watson in the middle, along with Patrick Ryder and Hurley up forward.
The Bombers then surged to a 28-point advantage when Heath Hocking booted a brilliant 50-metre running goal mid-way through second quarter.
Then Hurley snapped an extraordinary goal from hard up against the boundary.
It seemed the Swans might be involved in consecutive draws when the scores were level at the 15-minute mark of the final term, but instead they scored a gutsy victory.
Essendon 4.4 8.7 12.9 13.15 (93)
GOALS
Sydney Swans: McGlynn 3, Bolton 3, White 2, Bevan 2, Goodes, Kennedy, Rohan, O’Keefe
Essendon: Ryder 2, Crameri 2, Winderlich 2, Hurley 2, Jetta, Davey, Hocking, McVeigh
BEST
Sydney Swans: Goodes, Bevan, Bolton, McGlynn, O’Keefe, Grundy, Hannebery
Essendon: Watson, Stanton, Hurley, Heppell, Bellchambers, Ryder, Davey
INJURIES
Sydney Swans: Nil
Essendon: Hille (hip) replaced by Alwyn Davey
SUBSTITUTES
Sydney Swans: Craig Bird replaced by Brett Meredith in the last quarter
Essendon: Stewart Crameri replaced by Nathan Lovett-Murray in the last quarter
Reports: Nil
Umpires: Rosbury, Pannel, Jennings
Official crowd: 28, 082 at ANZ Stadium