England 2 for 192 (Cook 104*, Root 49*) trail Australia 327 (Warner 103, Smith 76, S Marsh 61, Broad 4-51, Anderson 3-61) by 135 runs
Melbourne: Alastair Cook made his first Ashes century for almost seven years to lead England's resurgence on day two of the Boxing Day Test in Melbourne.
The 33-year-old, in his 151st Test, reached his hundred in the final over of the day to take the tourists to 2-192, a deficit of 135 runs.
That came after Stuart Broad claimed 4-51 as the home side were bowled out for 327.
Australia, who have already secured the Ashes, looked set to push on from an overnight 3-244, with Steve Smith (76) and Shaun Marsh (61) extending their partnership past 100.
But when captain Smith became Tom Curran's first Test wicket, it began a slide that saw the hosts lose their last seven wickets for 67 runs.
On a slow surface, Cook blunted an Australia attack already without the injured Mitchell Starc and further weakened by a stomach upset suffered by Pat Cummins.
The left-hander passed 50 for the first time in six Tests, then had the good fortune of being dropped by Smith on 66.
When England won the Ashes down under in 2010-11, Cook piled on 766 runs but has not reached three figures against Australia since the final Test of that series.
Here, he played with increasing freedom as a crowd of 67,882 gradually emptied to leave the Barmy Army singing the former captain's name.
Cook shared an unbroken stand of 112 with successor Joe Root, who is 49 not out.
On day three, it will be the goal of the third-wicket pair, and the rest of England's batting line-up, to forge a lead large enough to negate batting last on a surface that is likely to get slower.
The failure of England's senior players on this tour has been a key factor in relinquishing the urn.
Before this Test, Broad had taken only five wickets and Cook had mustered 83 runs in six innings.
Indeed, ex-captain Michael Vaughan had questioned Broad's place in the side, while former spinner Graeme Swann doubted the "longevity" left in Cook's international career.
Broad, though, responded by picking up his best figures for a year and Cook showed his trademark patience, composure and judgement to sap Australia's bowlers in temperatures in the mid-30s.