The opener started the day on 104 but ended it with a towering and unbeaten 244 as he led them to a 164-runs lead.
And in doing so Cook helped himself to a host of new records.
This second double century on Australian soil was the highest score by a visiting batsman eclipsing Viv Richards’ 208 here in 1984.
It placed Cook in exalted company indeed with just Wally Hammond and Brian Lara having achieved it before.
Most importantly of all, his innings carried him past Mahela Jayawardene, Shivnarine Chanderpaul and Lara into sixth in the list of Test run scorers.
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The records tumbled regularly through the day as Cook relentlessly built his total.
But things might have been different had Australia held the chances they carved out – Steve Smith adding to his drop the previous evening when Cook had 66, by spilling the England opener when he had 153.
If the first was difficult, the second at square leg was easier, Smith going with his left hand only when two would have been possible.
Had Smith held that chance when England still trailed by nine runs – they were 318-6 at the time – the picture could have looked very different.
But with several useful partnerships stitched around Cook’s monumental knock, England were able to climb to a commanding halfway position.
Cook and Joe Root added 26 to their 138-run partnership before the England captain once again fell between 50 and three figures – a trend that it becoming alarming.
Just five of the last 27 half centuries for Root have been converted.
Root was furious with himself hoiking a top edge off a wide ball from Pat Cummins outside off stump, high to square leg where Nathan Lyon took an easy catch.
The England skipper’s mood had improved by the end of the day as Cook anchored England’s climb to a position of dominance.
Jonny Bairstow (22) and Moeen Ali (20) with a frenzied 14-ball cameo were disappointing, but Chris Woakes, who put on 59 for the seventh wicket and Stuart Broad who helped add 100 for the ninth, surpassed expectations.
Broad has struggled with the short ball so far this series and was struck on the shoulder early in his innings by Josh Hazlewood.
But the England bowler showcased his all too infrequently seen batting credentials with a flamboyant 56.
Cook and Broad lifted England to a 146 runs lead before they were separated, Usman Khawaja taking a superb diving catch at third man to dismiss the latter, a decision confirmed after replays showed the fielder had spilled but reclaimed the ball before it touched grass.
Jimmy Anderson stuck around without scoring to help Cook add a further 18 before the close.