Crawley created more clear-cut chances and Mike Jones was wastefully off target at the far post from Mustapha Dumbuya's cross.
Jamie Proctor's cross was then deflected on to his own crossbar by County defender Haydn Hollis in the 69th minute.
Crawley threatened early on when a goal-bound 20-yard shot by former Swansea striker Proctor was turned round the post by visiting goalkeeper Bartosz Bialkowski.
Bialkowski twice denied Jake Taylor and smothered Matt Sparrow's close range effort.
Notts midfielder Gary Liddle was booked for chopping down Nicky Adams just before the interval and from the resulting free-kick Sparrow blazed wastefully over.
Crawley continued to carry the most threat after the break and Adams had a low shot saved after a surging run from Mike Jones.
Home manager Richie Barker introduced three attacking players in a bid to pep up his mis-firing front line, but the result leaves the Red Devils with only one win from their last 11 home league games.