Rovers were taking on an under-fire side who sacked former Leeds striker Harry Kewell after just 10 weeks in charge earlier this week.
But in their first game since the Australian’s departure, County put four past Grant McCann’s Rovers in a six-goal thriller at Meadow Lane.
Kristian Dennis bagged a hat-trick for the club, whilst Enzio Boldewijn also got on the scoresheet to leave the Yorkshire club third in Northern Group G.
Striker Alfie May grabbed a consolation brace but failed to spark a second-half revival.
McCann’s men found themselves behind in the 16th minute as the ball fell kindly for Dennis in the box to grab his first goal for the club.
Rovers immediately pushed for the equaliser as they looked to restore parity.
Danny Amos almost levelled when he fired against the crossbar.
And moments later May was thwarted by the on-rushing Ross Fitzsimons after a misplaced back pass left the hosts’ stopper in trouble.
County doubled their advantage with Dennis turning provider for Boldewijn to fire in the second.
Goalkeeper Ian Lawlor should have done better for the third as Dennis headed home five minutes before the break.
After the break May was denied by Fitzsimons but made no mistake a minute later as a cool finish reduced the arrears.
Niall Mason and May both hit efforts off target as Rovers desperately tried to get back in the game.
All hope was seemingly quashed when Mason felled Richard Duffy, with Dennis sending Lawlor the wrong way to complete his hat-trick.
With 20 minutes left May’s deflected header gave a glimpse of a comeback but failed to inspire Rovers to turn things around.
Mallik Wilks had an effort saved, whilst Will Longbottom and Tom Anderson missed the target as the visitors huffed and puffed to no avail.
Right at the death Wilks was denied by a fantastic Fitzsimons’s save.