Australia needed only 11.4 overs of the final day to seal a 218-run win over England in Adelaide and move 2-0 up in the Ashes series.
Rain delayed the start of play by 10 minutes but England, on 247-6 overnight and needing 531 for victory, went down swinging to 312 all out when the skies cleared.
Stuart Broad hooked the fourth ball of the day for six but was caught by Nathan Lyon on the square-leg boundary from the next delivery, another short one from Peter Siddle, attempting to repeat the stroke.
Matt Prior, on 31 at the start of the day, pulled and carved his way to an 88-ball half-century, the first time he has scored 50 for 17 innings, since a match-saving 110 not out in Auckland last March.
Graeme Swann (6) hung around for 14 balls before poking an edge to Michael Clarke at second slip in Ryan Harris' first over after he replaced man-of-the-match Mitchell Johnson.
Prior went for 69 in the next over, the fourth England batsman in the innings to be caught on the leg-side boundary and completing Siddle's haul of 4-57.
And Harris (3-54) finished off proceedings after just under an hour's play by having last man Monty Panesar (0) caught in the covers.
The series now moves on to Perth for the third Test from December 13-17 where Australia can reclaim the Ashes with another victory.
"We have to look hard into ourselves, deep into the inner soul and drag the performance out of ourselves," he told Sky Sports 2.
"A 2-0 lead is not insurmountable. It's a bit like football - if we get the next goal, it's vital.
"We can't mope about feeling sorry for ourselves. We have to hold our hands up and say we haven't been good enough.
"We have to drag the runs out of ourselves, drag the wickets out of ourselves.
"We've had a big hit - and if we believe that the Ashes are gone, they might as well be gone," he added.
"We've had two tough games and we haven't played well. That's the simple deal.
"We have to dust ourselves off and do what we can do, which is work bloody hard on our games and come out to Perth on Friday with that belief that we can do something.
"We need to put some pressure back on Australia."
Cook's opposite number Michael Clarke, meanwhile, refused to crow about his team's two easy victories.
"It's still the hardest game in the world," he said.
"It's enjoyable, there's no doubt about it. The thing that's most pleasing is we're finally getting the results."
Do you expect England to hit back in the third Ashes Test in Perth?
Yes, they can still turn the series around
No, they will get rolled again