The stoic opener emphatically bounced back after a lean run of scores to finish the day unconquered on 244 off 409 balls. At the close, England were 491 for nine.
Along the way, Cook surpassed the highest score by a visiting batsman in a Test match at the famous Melbourne Cricket Ground, bettering the 208 by West Indian great Viv Richards in 1984.
He earlier bettered Wally Hammond's 200 set back in 1928 as the highest Test score at the MCG by an Englishman.
Cook's fifth double-century in 151 Test matches also catapulted him above West Indian Brian Lara to become the sixth highest run-getter in Test cricket with 11,956.
Australia, who already have won back the Ashes with an unassailable 3-0 lead, looked unable to stop the flow of runs in the final session as Stuart Broad supported Cook to take the game away from the hosts.
Broad, who survived a series of hair-raising short-pitched balls, thrived in his partnership with Cook, pushing the tourists beyond 450 on a lifeless pitch.
It needed multiple replays before Broad was finally given out for 56 off 63 balls to a diving outfield catch by Usman Khawaja off Pat Cummins, ending a demoralising 100-run stand off 110 balls with Cook.
Smith's Double Drop
Cook cashed in on two dropped catches by Australia skipper Steve Smith along the way to continue the misery for the home side.
Smith, who dropped Cook on 66 in the slips on Wednesday, put down the former England skipper for the second time on 153 in a sharp right-handed chance at square leg.
The tourists lost seven wickets for 299 on the third day with captain Joe Root again failing to convert a half-century into three figures when he top-edged a hook shot off Cummins to Lyon at deep square leg.
Root reached his third half-century of the series but was clearly furious with himself when he holed out on 61 in the morning session.
Dawid Malan, a century-maker in the third Test in Perth, was out leg before wicket with Josh Hazlewood's second delivery of the second new ball for 14.
Malan conferred with Cook before deciding not to review, yet replays showed a distinct 'Hot Spot' nick on his bat which would have kept him at the crease if he had challenged the decision.
It follows James Vince's similar dismissal on Wednesday to Hazlewood for 17, when he also did not seek a review despite 'Hot Spot' showing a mark on his bat.
England lost two wickets in the middle session with Jonny Bairstow caught behind off Lyon for 22 and Moeen Ali lashing out for 20 off 14 balls.
It was the sixth time in seven innings in the series that Moeen had been dismissed by fellow off-spinner Lyon.
Chris Woakes gloved a Cummins bouncer to wicketkeeper Tim Paine for 26 shortly after tea, and debutant Tom Curran was caught behind off Hazlewood following a 'Hot Spot' review.
alastair cookAshes 2017australiaBoxing Day TestDawid MalanEnglandJames VinceJoe RootJosh HazlewoodMCGMelbourne Cricket GroundMoeen AliNathan LyonPat Cumminssteve smithstuart broadtom curranUsman KhawajaWally Hammond
First Published: December 28, 2017, 1:21 PM IST