Hayden combined with Andrew Symonds to get Australia off the hook after England had the home side on a shaky 84 for five in the morning session on Wednesday.
But as has happened so often in the series already wrapped up by the Aussies, England's bowlers failed to deliver the knockout blow.
Hayden and Symonds shared in an unbroken 142-run stand for the sixth wicket to take the game away from the tourists.
Hayden continued his love affair with the Melbourne Cricket Ground, scoring his fifth century in eight Tests to join Allan Border as Australia's fourth-highest century-maker behind current captain Ricky Ponting (33).
Only Ponting, Steve Waugh (32) and Don Bradman (29) have scored more Test centuries than Hayden, who with Border ranks as the top-scoring left-hander of Test hundreds for his country.
At tea, Australia were sailing along at 226 for five, a lead of 67, with Hayden unconquered on 109 off 189 balls with 11 boundaries and a six. Symonds was not out 61.
Defending a modest first innings 159, England shook up Australia before lunch taking the wickets of the three top-averaging batsmen, Ricky Ponting (7), Mike Hussey (6) and Michael Clarke (5) to have the home side under rare pressure.
All three went into the Melbourne Test boasting century-plus averages in the series -- Ponting (104.80), Hussey (138.33) and Clarke (124.33).
But Hayden and Symonds regained command of the innings, scoring 115 runs in the middle session.
Symonds, who went to the crease with a Test average of just 18 in 11 matches, took 21 balls to get off the mark but unleashed the full range of his trademark one-day international shots to drain England's confidence.
Earlier, skipper Andrew Flintoff removed Ponting cheaply in the seventh over of the day.
The Aussie skipper attempted to pull from well outside the off-stump only to sky a catch to Alastair Cook at mid-wicket.
Hussey was bowled between bat and pad by Matthew Hoggard with one that straightened on him.
It was the third time in the series that Hussey has been bowled in the series, twice by Hoggard and once by Flintoff.
Steve Harmison, who has failed to recapture the form of last year's Ashes series in England, produced a gem of a delivery to remove Clarke in the next over.
Harmison found extra bounce with his second ball to get an edge off Clarke's prodding bat for wicketkeeper Chris Read to take the catch and leave the Aussies at 84 for five and trailing England at that stage by 75 runs.