The Bombers trailed by 31 points at the 14-minute mark of the third term and, at the time, had kicked just one goal since the eight-minute mark of the first quarter.
But Essendon kicked the final three goals of the third term and carried the momentum into the last, piling on five goals to the Blues' two to record a stirring 11.11 (77) to 10.12 (72) win.
Five talking points: Essendon v Carlton
The Bombers had plenty of heroes.
There was Melksham, who kicked the game-winning goal from 45 metres at the 28-minute mark of the last term, and two of the game's last three goals, both of which put his side back in front.
There was Jason Winderlich, who ran past Carlton sub Chris Yarran like he was standing still to intercept a Blues kick out of defence and pass the ball to Melksham for the sealer.
And there was Jake Carlisle, who bounced back from a thrashing from Jarrad Waite in the first half to take a game-saving pack mark in the dying seconds that cemented the victory after a gripping final term.
Carlisle also gave the Bombers a spark after half time when sent forward, taking nine second-half marks and kicking a goal as Michael Hurley was pushed back in an attempt to quell the rampant Waite.
Click here to vote for the three best Essendon players from the game
Waite was absolutely outstanding for the Blues, kicking a career-best seven goals, including five in the first half.
The Blues would be bitterly disappointed to lose a game they led most of the night, but coach Mick Malthouse would have been proud of the fight they showed after the surging Bombers hit the front at the 13-minute mark of the final quarter.
They hit straight back through a goal to Waite and were not headed until Melksham's goal in the dying minutes.
Essendon's win was even more remarkable given their two senior midfielders, Jobe Watson and Brent Stanton, were well held by Jaryd Cachia and Ed Curnow respectively.
Dyson Heppell (28 possessions), David Zaharakis (23) and Brendon Goddard (23) helped pick up some of the slack for the Bombers.
Essendon coach James Hird said after the match the Bombers had been lucky not to be further behind at half time, but had played exhilarating football in their comeback and never lost faith they could turn the match around.
"We didn't have the spark in our game in the first half, and we were trying to create passages of play that weren't happening," Hird said.
"But the game turned our way. We started to get more creative with the ball, we used the ball better, we took more risks and the game opened up.
"As disappointing as the first half was, the second half was very exciting."
Hird was thrilled with the results of swapping Carlisle and Hurley from one end of the ground to the other for the second half, saying the versatility of his talls was something the he would continue to exploit.
For the Blues, skipper Marc Murphy was outstanding with a game-high 31 possessions, and he was well supported by Andrew Walker (28) and Bryce Gibbs (26). Lachie Henderson and Michael Jamison also defended stoutly all night.
Click here to vote for the three best Carlton players from the game
Malthouse lamented his team's inability to capitalise on its dominance of general play in the first half.
"We didn't put them away in the second quarter; 5.1 sounds good but we had … 13 inside 50s. A lot of them were there to be scored off and we didn't do it," Malthouse said after the match.
"You've got to put sides away. It's a moving target this game these days, because you've got quality sides who can go 'bang' and kick three or four goals or hold you (from kicking) three or four, so it becomes a double-whammy.
"We were playing one of the better sides in the competition."
The Bombers kicked the opening two goals of the game, but Carlton dominated the rest of the first half.
Initially the Blues struggled to capitalise on the scoreboard, with their delivery inside forward 50 letting them down.
Despite leading the inside 50 count 18-6 in the first term, the Blues kicked just 1.4 to go into quarter-time three points down.
But Waite imposed himself on the game in the second quarter, almost singlehandedly ensuring the Blues started to get reward for their effort.
Having kicked the Blues' only goal of the first term, Waite kicked the opening four of the second to give him the last five in the game to that point.
His seventh for the night gave the Blues a one-point lead with 10 minutes remaining, and after the teams traded behinds on two occasions, Melksham stepped up to deliver the decisive blow and improve Essendon’s record to 8-3 for the season.
With just their second loss in their last eight games, the crestfallen Blues drop to 6-5.
Bombers skipper Jobe Watson celebrates his side's comeback win over the Blues. Picture: AFL Media
ESSENDON 2.1 3.4 6.7 11.11 (77)
CARLTON 1.4 6.5 8.9 10.12 (72)
GOALS
Essendon: Melksham 3, Hocking, Hurley, Stanton, Crameri, Kommer, Howlett, Carlisle, Myers
Carlton: Waite 7, Murphy, Betts, Casboult
BEST
Essendon: Carlisle, Hocking, Heppell, Goddard, Fletcher, Melksham
Carlton: Waite, Henderson, Casboult, Murphy, Walker, Gibbs
INJURIES
Essendon: Nil
Carlton: Nil
SUBSTITUTES
Essendon: Alwyn Davey replaced by Will Hams at three-quarter time
Carlton: Mitch Robinson replaced by Chris Yarran at three-quarter time
Reports: Nil
Umpires: Rosebury, Meredith, Jeffery
Official crowd: 82,639 at the MCG
