Jordy Mayifuila stole the show with four expertly taken goals as Eric Kinder’s men fell to their heaviest defeat of the season.
Seko Fafana and City captain Marcos Lopes also found the scoresheet on a bitterly disappointing night for the Rovers youngsters.
The visitors made a blistering start and opened the scoring after just five minutes, when Mayifuila finished off a superb free-flowing team move with a low shot under Rovers goalkeeper David Raya.
It could have been 2-0 to City shortly after, when Olivier Ntcham flashed a powerful first-time effort narrowly wide of Raya’s left-hand upright.
But Rovers’ reprieve lasted barely four minutes, as Fafana doubled City’s advantage with an emphatic close-range finish from Drury’s accurate pull-back.
Raya made an excellent flying save to tip over Fafana’s long-range missile, and Devante Cole, son of former Rovers striker Andrew, fired over as City dominated.
Rovers' first real opportunity of the evening came after half an hour, when Bradley Bauress' corner was missed by City goalkeeper Ian Lawlor and headed wide at the back post by Darragh Lenihan.
City's pressure on the Rovers goal was relentless and Mayifuila spurned a great chance to make it 3-0 when he failed to connect with Drury's driven centre.
However, the third goal duly arrived just eight minutes after the restart.
Cole was brought down in the area by Will Beesley and Lopes stepped up to coolly send Raya the wrong way with the subsequent spot-kick.
City made it 4-0 just before the hour, when Mayifuila thumped an unstoppable 20-yard volley into the top corner past a helpless Raya.
Rovers fashioned an excellent opportunity to reduce the arrears on a rare foray into City territory, but Devarn Green blazed well over when clean through.
On 64 minutes, the irresistible Mayifuila completed his hat-trick when he lashed a fierce right-footed effort in off the underside of the crossbar.
It was 6-0 to City barely a minute later, Mayifuila capitalising on some lax defending to fire a crisp low drive into the bottom corner.
Substitute Robbie Cotton was denied by Lawlor as Rovers pushed in vain for a consolation goal.
The menacing Drury struck the outside of the post with a venomous strike late on, but 6-0 was how it finished.
ROVERS: Raya, Fernandez, Beesley, Tanner (sub Doyle 84 min), Tumwa, Lenihan (c), Paulo Jorge (sub Cotton 56 min), Payne, Rittenburg (sub Wall 75 min), Green, Bauress.
Subs not used: Williams, Joel.
MAN CITY: Lawlor, Drury, Tasende, Plummer, Denayer (sub Bossaerts 63 min), Bryan, Lopes (c), Fafana, Mayifuila, Ntcham, Cole (sub Byrne 63 min).
Subs not used: O’Brien, Glendon, Bytyqi.
Goals: Mayifuila 5, 59, 64, 65; Fofana 11; Lopes 53