Notts goalkeeper Kevin Pilkington was the first to be seriously tested in a contest which produced plenty of finishing opportunities.
A well struck drive by Ryan Harley from the edge of the box was well parried by Pilkington, while at the other end goalkeeper Paul Jones should have been left without a hope of saving with the game 16 minutes old.
The chance fell to Delroy Facey who wasted it by shooting straight at the keeper from ten yards - an amazing miss.
Exeter's 25th minute lead arose from a dubious and controversial penalty. Michael Johnson was adjudged by the assistant referee to have caught the heel of Adam Stansfield and from the spot-kick Pilkington went the wrong way with the result that Marcus Stewart netted with ease.
Jones was soon in action again at the other end producing a good save which resulted in a corner from which Johnson, up with his forwards, headed narrowly over.
But the equaliser could not be long delayed. Myles Weston produced a thrilling run and when the ball fell to Facey he needed two attempts at it from six yards, before driving the ball inside Jones's right-hand post.
The leveller was no more than Notts deserved, but Exeter struck back for the dangerous Harley to strike a post only three minutes before County nosed in front.
Again it was Weston with an electrifying burst who laid on the chance and Gavin Strachan, bursting into the penalty area, flashed his shot home from the edge of the area.
Strachan had to go off moments later, again with a hamstring problem to which he seems to be suspect.
The surprise was that Notts did not seal the win with a third goal. Adam Nowland chipped a delightful effort onto the bar and Facey, again one-on-one with the goalkeeper, drove his shot at Jones once again.
It was the nearest either side came in a keenly fought second half.