The Swans killed off the game in the first quarter on Sunday at the MCG and eventually won by six goals and sealed two home finals with one round left.
But the 17.10 (112) to 11.10 (76) win was also notable for how the last-placed Bombers scrapped after their poor start, outscoring the Swans by one point over the next three quarters.
McVeigh is among the four candidates at Essendon, along with James Hird, Jaymie Graham and Murray Davis, and a decision is imminent.
With Sydney's finals series only three weeks away, coach Dean Cox said they are ready for the Essendon decision.
"That's one thing this football club has done well for a long period ... be ready for the unexpected or if something does arise," Cox said.
"We've had those meetings, discussions - we're really clear on what will happen if he (McVeigh) was, or wasn't, to get the position."
Cox and Bombers interim coach Dean Solomon were left frustrated by the game - the Swans coach because of his side's inconsistency, his Essendon counterpart because of their poor start.
"It's something we need to make sure we can rectify - you don't want to be flirting with anything or any form at this time of year," Cox said.
"My philosophy on this game is you earn every win, no matter how they come. You need to celebrate that, work on areas that you want to try to improve.
"That's what our football club is about, (it's) to play finals.
"We need to get back to playing our best football, but we've shown over 23 rounds so far that our best is good enough."
Solomon said Essendon continued to suffer from bad starts.
"It's almost like we need the opposition to punch us in the face and then we get going, which is not how it works," he said.
But Solomon said there were plenty of positive signs, given they matched the second-placed Swans for the rest of the game.
"Gritty, not pretty, is the style," he said.
The crowd of 24,767 was Essendon's lowest at the MCG in 33 years and Solomon called on the Bombers fans to show up next Sunday at Marvel Stadium for their season-ending game against Port Adelaide.
Not only are Essendon trying to avoid the club's worst season, it is also the 200th game for captain Andy McGrath.
"It's critically important we honour Andy and we make sure we carry him off at the end of the year," Solomon said.
"I'm a proud person ... we'll be doing everything we can to ensure we don't get that title (worst Essendon side) next to our names.
"I shouldn't probably say this, but it's really disappointing to see our crowds down. This is where we dig in and support each other ... we wade through the swamp together in the tough times."
Sydney spearhead Charlie Curnow kicked four goals, putting him on the verge of his third Coleman Medal, while Errol Gulden racked up a career-best 47 disposals.
Isaac Heeney, Logan McDonald and Chad Warner also showed their class.
When former Victorian Sheffield Shield fielding substitute Billy Coote kicked his first AFL goal on debut at the start of the second term, Sydney led by 44 points and a blowout was in process.
But the Bombers rallied and trailled by only 11 points in the third term before Sydney went up a gear and kicked clear.
Essendon fourth-gamer Vigo Visentini was a revelation in the ruck, delighting the Bombers fans with a couple of big tackles.
Nate Caddy kicked three goals for Essendon and Will Setterfield impressed through the midfield.
10°C