The Owen Burrows-trained juvenile was third behind high-class filly Nyaleti on his racecourse debut at Salisbury in June and confirmed that promise with a dominant success at Newmarket last month.
With Demons Rock the 6-4 favourite to secure a fifth consecutive victory, Hamdan Al Maktoum's Shabaaby was second best in the market at 13-8, but the result was scarcely in doubt.
Champion jockey Jim Crowley settled his mount in behind Beatbox Rhythm for much of the six-furlong journey and once given his head, Shabaaby shot clear to score by seven lengths.
John Kirkup came through to beat Beatbox Rhythm to the runner-up spot, while Demons Rock was a bitterly disappointing last of four runners.
Burrows said: "He's done that very nicely and he's improving with every run, which is great.The son of Kyllachy built on last month's Newmarket win on Town Moor (PA)
"He's a very straightforward horse. He settles well and when you pull him out, he's got a fair amount of gears.
"Originally we mentioned that might be it for the season. He's proved he handles plenty of cut in the ground. I'll have a chat with the team, they're back from Keeneland tomorrow and we'll see."
Nobleman's Nest got back on the winning trail in the Owlerton Greyhound Stadium Nursery.
Beaten just a nose into second place on his introduction here in July, the son of Poet's Voice readily went one better at Newmarket next time, but last month's Gimcrack at York proved a bridge too far.
Dropping into handicap company, Simon Crisford's colt was the 5-2 market leader under Silvestre de Sousa and comfortably put his rivals to bed with a length-and-a-half verdict. Crownthorpe was a clear runner-up ahead of Placebo Effect in third.
"York was a massive disappointment and we couldn't work out why he ran so badly," said Crisford.
"He only ran for two furlongs and I don't know what happened there. We came here still with lots of belief in him and fancied him to win, and he did.
"He travelled well, put that race to bed very quickly and he's a nice, straightforward and uncomplicated colt.
"We might find a Listed race somewhere, we'll see how much he goes up in the ratings. There might be another nursery in him yet, you never know."