Only 20.3 overs were possible on the fifth and final day, but that was still long enough for England to collapse to 37 for three, having been set 332 to win after Australia declared on their overnight 172 for seven.
But England, 2-0 up in the five-match series after wins by 14 runs and 347 runs at Trent Bridge and Lord's respectively, only had to draw this match to be sure of retaining the Ashes.
And they had the result they required when the match was abandoned as a draw at 4:39pm local time (1539GMT).
Earlier, Ryan Harris struck twice in quick succession to remove England captain Alastair Cook and Jonathan Trott before Peter Siddle claimed the prize wicket of Kevin Pietersen.
However, the bad weather for which Manchester venue Old Trafford is infamous, but which had stayed away until Sunday evening, took charge.
At the close, England were 295 runs shy of the victory target, with Joe Root, dropped on four, 13 not out and Ian Bell four not out.
Now the best Australia can hope for is to share the series 2-2.
In the event of a drawn campaign, the team that last won the Ashes retains them and in this series that means England following their 3-1 win in Australia in 2010/11.
One consolation for Australia was that this result ended a run of six successive Test defeats, their worst for 29 years, and meant they avoided equaling their all-time record losing streak of seven set between 1885-88.
Australia captain Michael Clarke, who made a superb first innings 187, was angry when the umpires took the players off for bad light on Sunday before rain ended the day's play.
The weather was still against Australia when rain delayed Monday's scheduled start by 30 minutes.
Harris, though, brought one back late into left-hander Cook to have him lbw for nought, with England yet to score a run.
Cook reviewed Tony Hill's decision but with nothing to suggest an incorrect decision, the New Zealand umpire's verdict was upheld.
Trott survived a leg before appeal from Harris when on nine, a decision the Australians reviewed only to be defeated by a marginal 'umpire's call' verdict after replays showed the ball taking the outside part of leg stump.
But Trott was out for 11 when he carelessly glanced Harris and was caught down the legside by wicketkeeper Brad Haddin.
Australia nearly had a third wicket when Root, who'd taken 26 balls to get off the mark, edged Siddle's sixth ball only for the normally reliable Clarke to drop the second slip chance.
But Siddle had the huge compensation of having Pietersen, who made 113 in the first innings, caught behind for just eight as he pushed forward.
Pietersen challenged the decision and while the audio part of the Decision Review System indicated a noise, there was no mark on the Hot Spot thermal imaging device.
However, Sri Lankan third umpire Kumar Dharmasena, in the latest contentious DRS judgment this series, decided there was insufficient evidence to overturn Hill's original verdict and England were 27 for three, with no reviews left.
Australia were now well-placed to press for victory, only for the weather to intervene again.
After rain delayed the start of the second session, Siddle struck Bell on the thumb with the third ball following lunch.
But as Bell received on-field treatment, more rain fell and play was suspended.
The series, which could yet see the first drawn Test campaign between England and Australia since 1972, continues Friday with the fourth Test at Chester-le-Street, the first Ashes match to be staged at the headquarters of north-east county Durham.
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