Set an intimidating 299 to win, the task was never going to be easy for the tourists.
From there, the wheels fell off and Australia couldn't recover.
England had already retained the Ashes, but they won the series after recording an emphatic 74-run victory in the fourth Test.
Australia went from 0-109 after 29 overs to all out 224 off 68.3 overs.
Even after Rogers (49) and Warner (71) fell, Australia were well positioned at 2-168 with 131 left to win.
But after spinner Graeme Swann laid the groundwork, Tim Bresnan got the key wicket of Warner and then Stuart Broad (6-50) ripped the heart out of Australia, inspiring a landslide that included skipper Michael Clarke and yielded 5-13 in 54 minutes.
There was to be no tail-end heroics and Australia's final eight wickets fell for 56 runs in under two hours.
A match that was set for a thrilling final day climax reminiscent of Trent Bridge, was over before it got dark on day four in Durham.
England might have already retained the Ashes at Old Trafford, but there was a moral victory on offer for Australia in Durham.
Instead, their morale was steam rolled as they went 3-0 down with one Test still to play and Shane Watson nursing a groin and hip injury.
Australia have now gone winless in their last eight Tests - their dominant effort at Old Trafford counting for nothing. Should they fail to win at The Oval they will drop to fifth on the ICC rankings.
Watson and Brad Haddin were given out for line-ball lbw decisions for the sixth and seventh wicket, with both batsmen disappointed as they walked from the field.
Australia used up their reviews and both came back umpire's call.
Both clearly felt the benefit of the doubt hadn't gone with them in the first instance.
However, England were already on a roll and the end seemed inevitable.
The damage was done once Alastair Cook brought about a double bowling change to replace a tired Swann (2-53) and a struggling James Anderson with Bresnan (2-36) and Broad in the 44th over.
Bresnan pitched up at a great length and Warner, sucked into the shot, edged behind.
It brought an end to an excellent innings which featured 10 fours and one six balanced out by great control.
But unfortunately it triggered an all-too-familiar collapse.
Michael Clarke (21) copped a jaffa from a fire-breathing Broad, and two overs later Steve Smith (2) inexplicably dragged a pull shot back onto his stumps.
It was a bitter blow for Harris who earlier with the ball had taken career-best figures of 7-117 and nine for the match in a classy display.
England were bowled out for 330 led by an Ian Bell 113, but Australia were left to rue 79 runs put on by the last three wickets.
Australia's batting was once again to blame - Rogers and Watson rescued them from a small total in the first innings and in the second dig it was only Watson and Rogers who showed any real resilience.
Usman Khawaja (21) was the second wicket to fall.
Khawaja was helpless against a full ball from Swann and trapped lbw, he fell victim to the England spinner for the fifth time in seven Ashes innings.
"It happens in the second innings of Test matches," said a despondent Clarke.
"I guess we would have liked to have scored more runs but it takes good execution with the ball.
"England's bowlers found reverse swing.
"Davey Warner and Chris Rogers played really well but unfortunately we couldn't do the same though the middle.
"I think it was still a pretty good batting wicket, it took some good bowling to find a way to break through.
"It was always going to be a tough chase but if we played the way we did in Manchester we would have had a real chance."
England captain Cook said his team showed remarkable composure to turn it around with nine wickets after tea.
"The skill to turn it around after tea was a great effort," he said.