Australia, in trouble at 84 for five chasing England's modest first innings of 159, rebounded ferociously with the two Queenslanders pounding the tourists' bowlers in a demoralising 279-run sixth-wicket partnership on Wednesday.
At the close, Australia had surged to a commanding 213-run lead at 372 for seven with three days to play. Symonds was unconquered on 154 in 316 minutes and Shane Warne was not out on four.
Hayden was finally out nearing stumps for 153, caught behind off Sajid Mahmood and compiled in seven hours off 265 balls with 13 boundaries and two sixes.
They were hundreds of contrasting significance, with Hayden taking his 27th to join Allan Border as Australia's fourth-highest century-maker, and Symonds releasing the demons of an unfulfilled Test career.
Hayden claimed his first century of the series and continued his fondness for the MCG, scoring his fifth century in eight Tests at the ground to rank with Border as the top-scoring left-hander of Test hundreds for his country.
Only current captain Ricky Ponting (33), Steve Waugh (32) and Don Bradman (29) have scored more Test centuries than Hayden in Australian cricket.
Meanwhile Hayden's long-time mate Symonds took 21 cautious balls to get off the mark before clubbing a 151-ball century sealed with a massive six straight over bowler Paul Collingwood's head. He finished the day with 15 boundaries and one six.
Symonds, who went to the crease with a mediocre Test average of just 18 in 11 matches, howled with delight and excitedly leapt into Hayden's arms to celebrate his maiden Test century.
The breakthrough hundred has probably booked his place in the crack Australian team for the immediate future.
Australia, stung by last year's series loss in England, regained the Ashes inside 15 days after winning the opening three Test matches and are trying to emulate Warwick Armstrong team's 5-0 Ashes sweep of 85 years ago.
Adam Gilchrist's boom and bust form continued when he was out for one caught in the slips off Mahmood nearing stumps after scoring a blazing unbeaten 102 off 59 balls in Perth.
As has happened so often in the series, England's bowlers failed to deliver the knockout blow when they had the home side in bother at 84 for five and the Test in the balance at 11:44 a.m. in the 26th over.
England shook up Australia before lunch taking the wickets of the three top-averaging batsmen, 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).
Skipper Andrew Flintoff removed Ponting cheaply when 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 Read to take the catch and leave the Aussies at 84 for five and trailing England at that stage by 75 runs.
The travelling Barmy Army supporters were in full voice, urging England to finish off the Australians, but Hayden and Symonds' deflating stand in almost five hours left them reflecting on more lost opportunities.
Jack Fingleton and Don Bradman hold the sixth wicket Ashes partnership at the ground with 346 in 1936-37.