The hosts should have won this more comfortably and seemed to be on their way to doing so after building up a 3-0 lead before half-time, thanks to a Michael Edwards goal and a brace from Dan Martin.
In the first half they clearly outclassed Accrington, whose back four really struggled to curb the lively Magpies.
Notts have developed a habit of scoring goals through defenders and midfield players and did so again here, as Martin, named as man of the match, played a role in all three County goals.
The stalemate was broken on 11 minutes when Martin's free-kick was converted by central defender Edwards, who scored off a post.
Martin's first was direct from a corner on 29 minutes. There was some question of a deflection by a visiting defender, but Martin said afterwards he had no hesitation in claiming it because the ball had already crossed the line.
There could be no dispute about his second and County's third on 36 minutes. He rifled in a low free-kick from 25 yards, with Accrington goalkeeper Ian Dunbavin poorly positioned.
Notts had other chances in the first half, at which stage it seemed only a matter of time before they added to their haul.
But in a lethargic second half in which the tempo of the game dropped alarmingly, the hosts completely failed to build on their advantage.
On the stroke of 90 minutes, a foul by Edwards gave Accrington a somewhat soft penalty, which Gary Roberts - the visitors' outstanding player - converted with a fierce drive.
Then, two minutes into stoppage-time, Paul Mullin accepted a short-range chance after Notts failed to get the ball clear.
It set up a tense last minute but Steve Thompson's Magpies survived to climb to seventh in the table.