Scoreboard
In the first innings, Alastair Cook set a number of records as he carried his bat to an unbeaten 244 in England's 491-run reply to Australia's first innings total of 327.
Earlier in the match, Stuart Broad repaid the faith of the English selectors, taking four wickets as Australia crumbled in their first innings.
After taking a modest five wickets in the first two tests of the series, Broad's position was in serious doubt after a horror 0-142 showing at the WACA.
Australian bowling great Glenn McGrath and former England skipper Michael Vaughan were among the most vocal critics calling for him to be dropped for the Melbourne test.
Broad, who has also struggled with a knee injury, bowled 414 balls without a wicket before he found the edge of Usman Khawaja's bat on Boxing Day.
After Australia resumed at 3-244, Broad bundled out Shaun Marsh (61), Pat Cummins (four) and Jackson Bird (four) to be England's best bowler with figures of 4-51 from 28 overs.
Earlier, Australian captain Steve Smith was dismissed for 76, chopping on from the bowling of English debutant Tom Curran.
The wicket was a much-needed one for England as Smith has dismantled them all series. With his departure, Australia were 265-4 after 97 overs. Mitchell Marsh followed soon after and England had fought back.
David Warner completed his first hundred of the Ashes series on Tuesday after getting a lucky break on 99 as Australia took the honors from England on the first day of the fourth test at the Melbourne Cricket Ground.
With the Ashes already back in Australia's hands after the home side easily won the first three matches of the five-test series, England toiled hard on a placid surface that offered little assistance to the bowlers but had little to show for their efforts against a ruthless opposition chasing a second straight sweep on home soil.
When play ended on day one, Australia was sailing along at 244 for three in its first innings with Smith not out 65 and Shaun Marsh with him on 31.
Warner laid the foundations for Australia's innings with an entertaining 103 after dominating a 122-run partnership with Cameron Bancroft (26), but England succeeded in putting the brakes on Australia's scoring when they removed both openers after lunch then Usman Khawaja (17) after tea.