Albeit too late for the series, much of this innings was the Brook England fans have asked for.
Coming in at 57-3, he eased to 20 from his first 30 balls with little alarm.
After an inside edge second ball narrowly missed his stumps, he dropped his next delivery into the off side and rotated the strike.
Across his 92 balls he defended or left 53% of deliveries on the classic ‘good length’ – a decent jump compared with the first four Tests of the series.
Brook appeared to be learning.
But things are rarely straightforward with England’s vice-captain.
At Melbourne he went beyond 3,000 Test runs in his 57th innings, a number only Herbert Sutcliffe can better for England, yet he still causes so much frustration.
He has reached 15 in seven of his eight previous innings of the tour without passing 51 – falling on at least two occasions to shots he himself described as “shocking”.
Here, having said in Adelaide he wanted to learn when best to apply the pressure, Brook reached the close unbeaten but so very nearly fell to another rush of blood.
Have you learned, Harry? Really?
Brook had 38 from 48 balls to his name when Australia turned to the most obvious of plans.
Captain Steve Smith and bowler Mitchell Starc stood together, five fielders were pushed into the shadows of the Sydney Cricket Ground’s famous stands and the ball was bowled short.
Australia knew what would happen next, England’s fans too. Brook can never resist.
Two balls into Australia’s Plan B, one that reduced the series’ best bowler in Starc to a battering ram, Brook backed away and almost top-edged a catch to the fielder lurking at third.
In Starc’s next over he got a warning when miscuing a pull shot towards mid-on, only to ignore it and repeat the shot from his next delivery.
The ball looped high into the sky but none of the three Australians positioned could cover the ground needed to complete the catch.
This time, Brook survived.
After getting through Starc, Brook misplaced another bouncer close to fine leg.
Then, rather than putting away the shot, he unfurled his full power to lift another from all-rounder Cameron Green into the stands.
It was a typical Brook response.
“I just didn’t feel like I was getting on top of the ball as well as I usually do,” he said.
“The wind was obviously going that way, so I just felt like everything was set up for me, and everything was coming through quicker when I started trying to go aerial.
“And if I get a little bit of bat on ball, then most of the time it’s going to go for six.”