England levelled the one-day series against Australia at 1-1 with a three-wicket win in the fourth match on Saturday.
Australia were bowled out for 227 in the 49th over before England reached their target with three balls to spare.
The final match of the series takes place in Southampton on Monday.
The first match was abandoned without a ball being bowled in Leeds while the third in Birmingham was declared a no-result.
Australia had won the second match by 88 runs in Manchester.