Brook, standing in for the injured Jos Buttler as skipper, blasted a maiden unbeaten ODI ton to beat the bad weather too on Tuesday, ensuring England were a commanding 46 runs ahead on the DLS method when the rains came to ruin the end of an an engrossing contest.
Australia badly missed their poorly star spinner Adam Zampa as the world champions' ODI win streak was ended at 14 matches, with England now back in business at 2-1 down in the five-match series and feeling confident for the two remaining matches, at Lord's on Friday and Bristol on Sunday.
England captain Harry Brook celebrates his century at the Riverside. (AP PHOTO)
England, chasing a tough-looking total of 7-304 headlined by another brilliant knock of 77no from Alex Carey, still ended up easing towards their target on 4-254, needing only 51 off 74 balls when rain started falling.
"Honestly, I thought 250 after our start would be awesome," said Marsh, who was also missing injured star opener Travis Head.
"For us to get to 300 was really good. We were well and truly in the game at halfway - but England were too good with the bat."
Asked about Zampa's illness absence, he added: "He's so valuable for us. We tried everything we had, but he was a big miss. We'll welcome him back in a few days time at Lord's."
Without the legspinner's mid-innings control and stand-breaking potential, Brook, still there on 110 off 94 balls, was aided by an excellent 84 off 82 from Will Jacks - the pair put on 156 for the third wicket - and a blistering late cameo from Liam Livingstone (33no off 20).
England's Jofra Archer celebrates after winning his duel with Steve Smith. (AP PHOTO)
After Marsh had lost yet another toss, the visitors, asked to bat by Brook under heavy skies and on a damp outfield, relied on two contrasting half-centuries from the in-form Carey and battling Steve Smith.
Carey followed his brilliant late, lone hand as player of the match in the win at Headingley on Saturday with another superb effort, helped in a fine late assault on the England seamers by the impressive Aaron Hardie, who hammered 44 off 26 balls before Carey left him high and dry in a final-over run-out.
Smith's 34th ODI fifty was a rare old struggle, with the master batter out of sorts for much of his innings before finally losing another engrossing duel with old foe Jofra Archer, dismissed for 60 off 82 balls.
Smith looked as if he had played his shot of the day when he pulled Archer with sweet timing in front of square only for Brydon Carse to somehow pull off a spectacular catch at full stretch on the boundary.
There were also valuable contributions from Cameron Green (42 off 49) and Glenn Maxwell, who clouted 30 off 25 balls.
Mitch Marsh was left hopping around a bit during his eventful knock of 24. (AP PHOTO)
The Aussies blasted 55 off the last four overs to reach a total 27 runs higher than the average first-innings score at the Riverside.
The captain himself had begun with a battling 24, even though he had to wear a couple of body blows from Archer in his first over and then another painful hit to the chest by Carse en route.
Smith's battle with his old tormentor Archer was also a treat, with the ever-animated batter at one point falling in undignified fashion on his backside trying to scoop the England pacer, before also later copping a blow to the shoulder.
When England batted, Mitchell Starc (2-63) snaffled two wickets in the first two overs, getting Phil Salt picked up with a mistimed flick to Matt Short at midwicket before Ben Duckett edged him to Maxwell at deep gully.
But then England's batting wasn't challenged much against some ordinary bowling, only Green (2-45) picking up Jacks and Jamie Smith with short-ball tactics.
