Two first-half goals by Lee Peacock set up a goal fest to underpin the belief of City's chairman that this will be a promotion season.
"I don't only think it, I know it," chairman Steve Lansdown told the fans. "My board have dipped into their own pockets to give us the strongest squad in the division and our wages are higher than many in the first." Third last season, the Bristol side had far too much clout for the league's oldest club, who are plagued by a cash crisis.
Caught up in a two-hour traffic jam, Notts only escaped an FA fine for handing in their teamsheet late by phoning it from their stranded coach.
The start was put back for five minutes, but their anguish soon followed them on to the pitch.
City's pressure had them on the back foot long before Peacock's first strike in the twelfth minute.
Picking up a ball from Mickey Bell he skipped round one defender before placing a low shot to the right of Notts' despairing keeper Stuart Garden.
Garden had a wretched time, his defence was cruelly exposed and his handling was unsure.
Many of County's problems stemmed from Luke Wilkshire, an Australian who quit Middlesbrough for the chance of regular football.
Nominally a right-flanker, he popped up all over the place but was shaded as man of the match by Peacock. Luck was with him for his second goal, a rather weak header from a Wilkshire corner which squirmed between two defenders and was over the line before being hooked out.
Notts' new striker Clive Platt, unable to sign a contract while the club are in administration, battled to get his latest club into the game.
With his long striding runs he kept home centre-back Tony Butler stretched while both Steve Jenkins and Ian Richardson planted long-range shots against City's bar.
County's hopes were quickly extinguished four minutes into the second half when Wilkshire set up City's other signing, Lee Miller from Falkirk, to volley the third goal.
The other came late on from sub Lee Matthews, who first capitalised on a Garden fumble and was then lurking perfectly at the far post to convert a Bell cross.