The result takes the Swans to 14-4 for the year and one victory ahead of both Hawthorn and Geelong, who play the Western Bulldogs and North Melbourne respectively this weekend.
Luke Parker (who had a career-best 35 possessions), Mike Pyke and Ben McGlynn were all excellent for the home side, with Adam Goodes, Kurt Tippett and McGlynn kicking two goals apiece in front of a healthy crowd of 36,804.
The Swans travel to Port Adelaide next week before closing their home and away season against St Kilda, the Bulldogs and Richmond.
"We got off to a good start in the first quarter and thought our pressure was pretty good.
"Conditions were pretty tough, it was pretty windy, so it was about getting the result. We persisted long enough to do that."
In a year that continues to be overshadowed by the supplements scandal and uncertainty over James Hird and Mark Thompson, the Bombers never gave in and were within 15 points deep into the final term.
But they couldn't get any closer, with a late Goodes goal sealing the Swans' 13th victory from their past 14 games as they bounced back from last week's loss to the Hawks.
Jake Carlisle (11 disposals, one goal), who had been in outstanding form over the past fortnight, was well held by Heath Grundy, while at the other end Michael Hurley (29 disposals, seven marks) was a clear standout.
Patrick Ryder (15 disposals, 28 hitouts, two goals) loomed as a potential match-winner for the Bombers, particularly in the third quarter, but he faded in the final term as the Bombers had their three-game winning streak snapped.
Dyson Heppell and Zach Merrett were also influential for an Essendon side that was far from outclassed, but still finds itself in a dogfight at the bottom half of the eight ahead of next week's Friday night clash with the Tigers.
Essendon dropped to 10-8 with the loss, with Adelaide a chance to leapfrog them on the ladder if they beat West Coast at home on Saturday afternoon.
The Swans dominated the opening exchanges and were far more potent going forward, kicking five goals to one in the first term for a healthy 26-point lead at the first change.
A strong breeze was making scoring difficult towards the Paddington end of the SCG, but the Bombers were unable to capitalise in the second quarter against a home side that wanted the ball more.
Whatever Bombers coach Thompson said at the main break had the desired effect, with Ryder rampant as the visitors kicked the first three goals of the quarter to close to within 10 points.
From that point on the Swans were always able to keep their noses in front as the premiership favourites banked another important four points.
Thompson felt his side had been fortunate to get as close as it did by full-time.
"We were lucky just to lose by the margin we did.
"But we haven't lost too much tonight. There's no shame in losing to Sydney."