Jeff Hughes gave the League One side the lead in the 37th minute when an Alan Sheehan free kick evaded everyone to find Hughes at the back post, who then controlled the ball before firing it into the far corner.
After the restart, Notts had to weather the storm as Doncaster looked for the equaliser. Kyle Bennett struck a wild shot from 25 yards that forced Notts County goalkeeper Stuart Nelson into making the save.
James Coppinger then thought he had drawn the sides level as his cross nearly found its way into the corner before Nelson pushed it wide. From the resulting corner Giles Barnes blazed a chance over the bar.
Doncaster were then dealt a blow when Sheehan was brought down by Sam Hird in the area, giving a Notts County a penalty in the 69th minute. Jeff Hughes slotted the penalty into the bottom right corner for his second of the game.
Doncaster continued to try to find a goal but Notts battled well to hold on for the win and a place in the fourth round draw.