On a chilly evening in Chester-le-Street, England warmed the hearts of the die-hard home fans. Late rain ended the match, but Harry Brooks' outstanding 110 points without defeat suggested progress and took a point back in what had been a one-sided series.

The two teams travel to Lord's on Friday for the fourth match, with Australia, now leading 2-1, no doubt keen to settle the matter on the pitch that caused a lot of trouble for some of them in last summer's Ashes. There was no such animosity at the Riverside, just 14,000 players in zip-up coats cheering England on to the finish line before a soggy finish and a Duckworth-Lewis-Stern method 46-run victory.

After Alex Carey fired back in with an unbeaten 77, England were left for 305. When Mitchell Starc routed Phil Salt and Ben Duckett with the new ball, England were beside themselves. But after a dangerous 11 for two in the third over and Will Jacks scoring a smooth 84 from No. 3, Brook took his side to 254 for four in the 38th over, ahead of quota, when the heavens opened.

With 13 fours and two sixes, and his maiden international one-day century from 87 balls when he smashed Starc through the empty slip area, this could well prove to be a significant innings for Brook. After all, as a number in this rebooted England team, the 25-year-old is mainly learning the rhythm of 50-over batting at the highest level due to the chaos that is the domestic schedule. Days like this are storehouses of experience.

They also reveal Brook's best qualities. The right-hander's thumping air-strikes and back-foot cuts were undoubtedly dazzling shots that mark him as one of the best ball-strikers on tour. But it was all based on a desire to keep a cool head at the plate and play the ball late, suggesting the “who cares?” comment he made after Trent Bridge wasn't entirely true.

“I think people took it a little bit the wrong way,” said Brook, who described this first win as interim coach primarily as a relief. “You have to go out there and play fearlessly and almost have that 'who cares?' attitude. But it's not 'who cares if we lose.' You just can't be afraid of being eliminated.”

This was also the Yorkshireman's first century against Australia in any format – a decent point to put behind him ahead of future major clashes – and it built on a rollicking stand of 156 off 147 balls in which Jacks took the first risks. Even after Cameron Green claimed a Surrey double by taking Jacks and Jamie Smith out with a couple of short balls, Liam Livingstone emerged in fine spirits to score 33 off 20 balls and give himself enough breathing room on DLS.

“All credit goes to Harry,” said Andrew McDonald, Australia's head coach. “He's an impressive player and has a long career ahead of him. He's going to give us a lot of headaches along the way. Sometimes you have to take your hat off to your opponent. This is one of those moments. The way he brought the game onto the ice was very impressive.”

McDonald went on to point out the difference in missing Adam Zampa, the leg-spinner the latest to succumb to illness in the tour camp. Travis Head was also rested, with Australia's 304 for seven runs owed more to a late acceleration than his breakneck starts. They were 200 for five with ten overs to go, but still managed to score another 104 runs through Carey's last silk kick and Aaron Hardie's 44 runs in 26 balls, which somewhat spoiled Jofra Archer's figures.

After a breather at Headingley, Archer had returned two for 36 in his first eight overs, dismissing Matthew Short early and taking Steve Smith out for 60 thanks to Brydon Carse's brilliant catch on the rope. Despite all the talk of a personal duel dating back to a bloodcurdling encounter in the Ashes five years ago, this was the first time Archer had taken Smith out in international cricket. The only mention of that day at Lord's came when Smith landed on his backside attempting a funky scoop.

But Archer's last two overs brought 31 runs, Hardie sending him to the stands twice as the radar failed to work. Brook admitted afterwards that he was a poor seamer, although Jacob Bethell and Jacks made up for this by taking out Green for 42 and Marnus Labuschagne for a duck. Carse was arguably the best player with 10 overs of power in which he worked Mitch Marsh superbly before finding the edge. Like Brook's innings, this seemed a moment that could have significance later.