Blackpool became the latest victims following earlier successes in this run against Tranmere, Bristol City and Bournemouth.
All have been achieved without conceding a goal, but this was the closest of the four.
The first ten minutes Notts started out the brighter and were on top of their game. But then they started to slack and take their foot off the gas as Blackpool got back into the match.
In the first half, their were few incidents, the one that stuck in my mind though was the blatent handball in the area by full back Leam Richardson. He seemed to stick his hand out while the ball came to him in mid air. It was the most obvious penalty decision i had ever seen.
Paul Heffernan had shaken off a challenge in pursuing a long through ball, and as Phil Barnes advanced from goal he took the ball round the goalkeeper and converted from the narrowest of angles off the inside of the back post.
But the referee had spotted an infringement for which he booked central defender Brian Reid, ruled out Heffernan's strike and pointed to the penalty spot.
It was a decision that could have denied Notts a goal, and penalised them rather than Blackpool, but Allsopp banished such thoughts by crashing the ball over the line via the underside of the bar.
It was the big Australian striker's 10th goal in nine matches, which have done much to ignite County's recovery bid.
He did not have a direct shot to deal with until the hour mark - then defender John O'Kane fired one which Garden handled competently.
First a high boot by defender Tommy Jaszczun caught the Notts winger full in the face, breaking his nose, yet went completely unpunished.
Moments later Cas went sprawling in the box. Although nearer to the incident, the referee nevertheless looked to his assistant, and with no flag shown waved play on.
Notts manage Bill Dearden raced down the touchline to make an unavailing protest.
A firm pitch and high swirling wind badly affected the quality of the play which was generally scrappy, but Notts held on in face of a late Blackpool rally and justified all three points.
An uninspiring display with Blackpool giving a decent account of themselves in the second half, but as Billy said Notts cannot afford to slack or take there foot off the pedal. In my opinion they need one more win to secure their second division status next season.