Australia offspinner Nathan Lyon celebrated his 100th test wicket in a 5-50 haul as the tourists lost their last five wickets for six runs, squandering a hard-fought advantage their bowlers had secured in the morning.
Chris Rogers was on 18 with fellow opener David Warner on 12 as Australia, chasing 231 for victory, reached 30 for no loss at the close of a blustery day's play in front of a crowd of more than 63,000.
"To have that result in the second innings for Australia is fantastic to turn the game around," Lyon told reporters.
"We didn't expect that, but we knew if we bowled in partnerships and keep on improving as a bowling unit then we knew that we could possibly crack open the game.
"Come tomorrow Australia has to be really patient with our batting and it's going to be a massive challenge."
Though victory and a 4-0 lead in the five-test series would seem Australia's for the taking, no team has ever chased down more than South Africa's 183 in 2008 since the first use of drop-in wickets at the MCG in 1996.
Both sides have struggled to score over 200 on a two-paced wicket amid Melbourne's notoriously fickle weather, which brought baking heat before a cool change ushered in chilly gusts and blew rubbish across the field late in the day.
England, however, were in large part the architects of their downfall in the second innings having pushed the lead to 116 without loss shortly after lunch.
England captain Alastair Cook had moved serenely to his third half-century and became the youngest cricketer at 29 to reach 8,000 test runs, but his wicket for 51 was duly followed by the loss of three more for one run in the session.
Rejuvenated seamer Mitchell Johnson firmed his bid for man-of-the-series by trapping Cook in front with a searing inswinger and finished with 3-25 after having wicketkeeper Jonny Bairstow caught behind for 21 and Monty Panesar lbw for a duck to wrap up the innings.
The 32-year-old left-armer also dismissed Joe Root for 15 with brilliant fielding, throwing down the stumps from mid-off with the England number three well short of his bid for a reckless single.
Two balls later Johnson, disbelievingly, took the simplest of catches at mid-off as Ian Bell lofted a horrid drive off the bowling of Lyon to be out for a golden duck.
That completed a collapse of 3-1, kicked off when paceman Peter Siddle trapped Michael Carberry in front after a dour knock that yielded only 12 runs from 81 balls.
England still held a lead of 182 after tea with six wickets in hand, but promptly imploded as Lyon combined with Johnson to mow through the tail.
Lyon struck to remove Ben Stokes for 19 to end a 44-run partnership with Kevin Pietersen, the spinner coaxing the all-rounder into a clumsy slog straight to Steven Smith at mid-on.
The 26-year-old struck again the second ball after drinks to bowl Tim Bresnan for a duck, and three balls later had his 100th when Stuart Broad was out for another duck by offering up a catch to Australia captain Michael Clarke at slip.
Lyon capped a banner day by dismissing Pietersen for 49 for his fifth wicket when the South Africa-born batsman slogged to Ryan Harris at long-off.
While Lyon enjoyed most of the plaudits, Haddin continued to be the thorn in England's side, with his first innings 65 making him the first batsman at seventh or lower in the order to post four first innings half-centuries in a series.
He also surpassed Englishman Alec Stewart's 378 runs on home soil in 1993 to become the highest-scoring wicketkeeper in an Ashes series, and his last wicket stand with Lyon added a valuable 40 runs.
James Anderson was the pick of England's bowlers with 4-67, with Broad taking 3-45, and Cook will lean heavily on his two seamers to back up and win the match for England.
"I'm not really sure that I can explain what happened (with the batting) if I'm honest but obviously it was disappointing," Bairstow, who replaced the dropped Matt Prior behind the stumps, said.
"The mood is (we're) looking forward to tomorrow. I guess it's an exciting challenge knowing we've got to go out and take 10 wickets.
"Very confident (of victory). We've got people in our side that have shown over a number of years the skills that are needed tomorrow to win us this game of cricket ... We're still 200 runs in front."