Brook's hundred sees England beat Australia to remain in series
Victory at Chester-le-Street kept England alive in a five-match series at 2-1 down with two to play.
England slumped to 11-2, chasing 305 to win, after left-arm fast bowler Mitchell Starc removed openers Phil Salt (nought) and Ben Duckett (eight) in the space of four balls.
But Will Jacks (84) and Brook (110 not out) responded to the pressure of the situation by adding 156, with the third-wicket duo showing good judgement as well as shot-making skill.
Rain stopped play with England closing in on victory at 254-4 off 37.4 overs.
But they were 46 runs ahead of where they needed to be under the Duckworth-Lewis-Stern method for rain-affected matches.
And with a downpour meaning no more play was possible, it meant England had ended Australia's run of 14 consecutive ODI wins.
Earlier, Australia made 304-7 after Brook won the toss.
Alex Carey was 77 not out, with star batsman Steven Smith making 60. England fast bowler Jofra Archer took 2-67.
The series continues at Lord's on Friday.