His counterpart Michael Clarke keeps chin up to fancy an Australian comeback from 2-0 down in the series.
Alastair Cook savours graft in craft of winning second Ashes Test
Graeme Swann struck in the nick of time to complete England's 347-run victory inside four days, and ensure they moved 2-0 up in the Ashes series.
Australia's last pair of Ryan Harris and James Pattinson took their hosts to within three deliveries - even after an extra half-hour - of having to return to complete a final-day formality in the second Test.
Instead, after Joe Root had added two telling wickets to his 180 runs, England are already within one more Test success of winning the Ashes next month for a third consecutive time.
Sputtering Australia always appeared certain losers at some stage - especially after three wickets went for 12 runs before lunch and then three more for just two almost on the stroke of tea.
But numbers 10 and 11, stubborn in the extreme after 30 runs had also been added for the ninth wicket, defied England for more than an hour and 14 overs until Pattinson was lbw on the back-foot defence to become Swann's ninth wicket of the match as Australia were dismissed for 235.
Cook told Sky Sports after seeing England snatch victory in the final over of the fourth day: "It was obviously a bit of hard work and we just about got there in the end.
"We've played some pretty good cricket over these two weeks. We've also had to scrap very hard in this game, being 30 for three in both innings - people have had to stand up with the bat and deliver.
"Belly's [Ian Bell] hundred in the first innings and Rooty's hundred in the second innings when they were under pressure at the start was fantastic.
"And obviously the bowlers have done a great job in both of these matches."
There was still plenty of graft ahead for the hosts to take four more wickets, particularly as those 73 runs were added for the last two, but they just about managed to eke their way through the tail. England had declared on 349 for seven, and then unleashed Swann to help close out victory on a wearing pitch.
James Anderson gave them their first breakthrough, Shane Watson lbw in predictable fashion - for the 10th time in 19 innings against England - pushing forward in defence but missing an inswinger.
Swann was called into the attack in the 10th over, and England's most obvious wicket-taker in these conditions struck for the first time with only his fifth delivery. Australia's legion of left-handers had a tough time with Swann bowling in the rough.
Chris Rogers and Phillip Hughes perished to Swann in quick succession, as Australia went into lunch at 36 for three.
Australia held on for a while but Root came back to torment them with the ball. The part-time offspinner claimed the valuable wickets of Michael Clarke (51) and Usman Khawaja (54), triggering three wickets to fall with addition of as many runs.
The last wicket pair added 43 runs to frustrate England, but in the end, Swann struck with three balls remaining.
Root was named man of the match. Cook was full of praise for Root's "fantastic" century, while insisting there is still plenty more to come from the young opener.
Cook said of the young opener, 22, who was promoted in place of the regular Nick Compton at the start of the series: "It was a great knock.
"He was under pressure in that second innings. Obviously, he's had a bit of success at No 5 and it's slightly different at the top of the order, but we all know what a great player he is.
"He's still got a huge amount of work to do, but he's the right character at the top of the order and it was a fantastic knock."
England lost Kevin Pietersen to a calf strain following Day 3, but Cook hopes the batsman will be fit for the third Test at Old Trafford, which starts on August 1.
"It's just a strain. Thankfully it's not a tear," the skipper said.
Despite going 2-0 down in the five-match series, Australia captain Michael Clarke refused to give up hope that his side could yet win back the Ashes. "It was certainly not the performance we were after but we've got some time now to make amends I guess," he said following today's loss.
"We'll continue to work hard in the nets and try and get right for Manchester. We know we've got to win the next three Tests to win this series, so it's very clear for us now."
Asked if he thought that was a realistic target, Clarke added: "Of course it is. I think it's going to be hard, there's no doubt about it, but I'd be silly to go into Manchester expecting to lose."
Evidence seems to suggest that it remains a strong possibility.
"We'll do everything in our power to try and improve our game, because we need to do that, especially our batting," Clarke said.
"But take nothing away from England. I thought they outperformed us again in this Test."
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