The only goal of the game came in the first half as Jake Day converted from the penalty spot.
Basford started on the front and in just the fifth minute of the game they came close to taking the lead. A poor clearance was seized upon by James Carvell and he played in Marcus Marshall but he could not keep his effort down.
A free-kick was then saved by Kieran Preston before Niall Towle stung the palms of George Willis with a powerful effort. On 25 minutes the game looked to have its first goal when Towle tapped the ball in at the back post but it was ruled out for offside.
Straight up the other end Day forced Preston into a good save before the referee pointed to the spot for a foul against Ryan Wilson. Day stepped up to smash the National League side into the lead.
Eight minutes from the break it should have been 1-1. Striker Towle was played through on goal but his low effort was saved by the feet off Willis, which saw Alfreton maintain their advantage at the break.
Within ten minutes of the restart Basford went close to drawing level. A corner from the right was headed goalwards but the visitors had a man on the line to clear the ball off the line. Just after the hour mark Towle was in on goal and he opted to shoot from a tight angle, rather than squaring for Marshall, and the effort was high and wide of the target.
The pair were then involved again as Basford had their best chance of the half. Marshall did well down the left to pick out Towle in the middle, whose header beat the Alfreton ‘keeper but bounced just wide of the post.
James Clifton was the next Basford player to go close but his effort was dragged wide of the post after the defender was picked out by James Carvell in the middle. The hosts continued to look the more likely to score as Rev James burst into the area but the final product was lacking as the forward was dispossessed.
A free-kick with just three minutes left saw Alfreton strike the post, in what was their first real goal scoring opportunity of the half. Straight up the other end Basford had another great chance. The ball came across the box into the path of Kyle Dixon but his low effort was cleared off the line as Alfreton held out for a 1-0 win.
Starting XI: 1- Preston (Pierrepont), 2- Roma (James), 3- Wilson, 4- Dunn (Tague), 5- Galinksi, 6- Betts (Carr), 7- Clifton, 8- Chettle (Dixon), 9- Marshall (Gatter), 10- Towle, 11- Carv