City were good value for their win and it was their sixth visit to Notts without defeat.
Notts were sluggish from the start and Chester began to take control.
However, when the opening goal came it was of the speculative variety.
Burly frontman Jon Walters received the ball only a few yards in the home half of the field but, spotting goalkeeper Kevin Pilkington off his line, drilled a low shot inside the left-hand post.
How it did not become a 2-0 lead six minutes later was a complete mystery.
An error by David Pipe presented the ball to Gregg Blundell who, like Walters earlier, also spotted Pilkington off his line. He too tried from long range instead of making sure and a poor shot flew into the crowd behind the goal.
Notts, probably unable to believe their good fortune, began to raise their game and as has often been the case this season found a goal from a set-piece.
Right on half-time dead ball specialist Ian Ross floated a free-kick to the back post where Jason Lee headed home sharply.
After some strong words in the dressing room at half-time, Notts improved without ever dominating in the second period.
It was a goal similar to County's when Chester went back in front on 79 minutes.
Roberto Martinez delivered a classic corner to the back post where Ashley Westwood met it with a firm header.
Without ever convincing, Notts struggled to find a second equaliser and substitute Junior Mendes had a shot blocked before Lee drove wide.
In the remaining few minutes, however, Chester were well on top and Notts slumped to a third consecutive home defeat and their sixth of the season in the league in front of their own fans.
Hardly surprisingly, they were booed off at the finish.