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.
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 equalling 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 yesterday before rain ended the day's play. The weather was still against Australia when rain delayed final day's scheduled start by 30 minutes.
The fourth Test starts on August 9 at Chester-le-Street.