Hille booted three goals in the final term as the Bombers overcame a dreadful third quarter to end Melbourne's season with a 15.14 (104) to 15.9 (99) victory before nearly 61,000 fans - the biggest crowd of the 2004 season.
The victory means the Bombers advance to next week's semi-finals where they will play the loser of Sunday's qualifying final between Port Adelaide and Geelong.
But for Melbourne, its season is over, just five weeks after they were on top of the ladder.
However five straight defeats since then have ended the Demons' season and it is the first time since they re-emerged into the finals in 1987, after 23 years in the wilderness, that Melbourne has been eliminated in the first week of the finals.
But the Demons went down fighting and their disappointed supporters could well be entitled to ask whether their team would have won had skipper David Neitz not been a late withdrawal due to a calf injury.
With Neitz watching from the grandstand, the Demons just did not have any key forwards all day and it was only a great performance after half-time from Russell Robertson that enabled Neale Daniher's side to storm back into the game.
The Demons looked gone when they trailed by 31 points at half-time but seven goals to nil in the third term saw them go into the last change with an eight point lead.
But in a heart-stopping final term it was the unheralded Hille, who proved the difference between the sides.
He booted the opening goal of the final term to level the scores at the seven minute mark and after Robertson had goaled to put the Demons back in front, Scott Lucas goaled to again level the scores just a minute later as the tempo rose considerably.
But Hille then marked again and goaled from a tight angle at the 18 minute mark to regain the lead for the Bombers but again Melbourne came back to hit the front by a point when Phillip Read goaled at the 20 minute mark.
However Hille was determined to have the last word and he delivered the winning goal at the 23 minute mark when he soccered one through from the goalsquare after outwitting Melbourne full-back Alistair Nicholson in a one-on-one battle.
Defeat was tough on the Demons but it would have equally been tough on the Bombers with both teams producing a magnificent contest.
The Bombers twice threw away major advantages with the Demons fighting back to level the scores at quarter-time after Essendon had led by four goals in the opening term.
And then after Essendon dominated the second term to lead by more than five goals at half-time, Melbourne seized control of the game in the third term as both teams took it in turns to have the momentum.
But with midfielders of both sides producing heroics - with Jason Johnson, Dean Solomon and Justin Murphy all terrific players for Essendon and James McDonald and Nathan Brown continually surging Melbourne forward - it was Essendon's superior attack which proved the difference.
While Melbourne had to rely on midfielders such as Adem Yze to kick their goals - and Yze and Travis Johnstone could hardly have done more given they had 48 touches and kicked five goals between them - Essendon had plenty of options in attack.
Champion full-forward Matthew Lloyd booted four to take his season's tally to 93 while Lucas was also dangerous after moving forward in the final term.
And skipper James Hird led by example after overcoming a heavy knock from Matthew Whelan in the first term and his great mark on the outer wing in the dying seconds sealed victory.
In contrast Melbourne skipper David Neitz could only watch on in frustration and his calf injury certainly could not have come at a worse time for his club.
Essendon coach Kevin Sheedy said reverting to a more direct style of play in the final term had proved the difference.
"We had to use the ball better (in the final quarter)," Sheedy said.
"We overused the ball in the third quarter, we had more handballs than kicks and I don’t know why players do that."
"We held up the figures to them at three-quarter-time and it’s amazing what you can when you get the ball down there (the forward line) quickly."
Melbourne coach Neale Daniher said his developing team can build on its performance this year, despite its inability to peak at the business end.
"We're bitterly disappointed today. We had a chance to win the game and our own use of the footy cost us the game," Daniher said.
"In 2002 we won our first final and just fell short a little bit like this game.
"We're not a premiership team, so it's not a wasted year. It's been a development year for us and we come out of the year with a lot of lessons. You've got to play to the line, it's a long season (and) you've got to be up at this point of the year.
"There's a lot of positives that come out of our season from the point of developing a team."
Melbourne: 5.2 6.5 13.6 15.9 (99)
Essendon: 5.2 11.6 11.10 15.14 (104)
Goals: Melbourne: Yze 3, Robertson 3, Johnstone 2, Green 2, Read 2, Bruce, White, Rigoni
Essendon: Lloyd 4, Hille 3, Hird 2, M Johnson, Watson, McVeigh, J Johnson, Bolton, Lucas
Best: Melbourne: Yze, McDonald, Robertson, Johnstone, Miller, Brown, Rivers Essendon: J Johnson, Solomon, Murphy, Hille, Hird, Lloyd, Lucas, M Johnson
Hasleby, Webster, Headland, Pavlich, Haddrill
Injuries: Melbourne: Neitz (calf) replaced in selected side by Rigoni.
Essendon: Rioli (hamstring) replaced in selected side by Bullen.
Reports: Nil.
Umpires: James, Kennedy, Rowe
Crowd: 60,903 at MCG
