Hereford goalkeeper Dave Cornell pulled off a string of excellent saves in the first half as the hosts came under heavy pressure. But the on-loan Swansea stopper was left exposed after 19 minutes when a neat interchange between Danny Hylton and Rankine left the latter to finish neatly.
United, playing against a strong wind, had their work cut against a powerful Aldershot defence which was organised by former Bull Darren Jones. But Tom Barkhuizen forced an excellent diving save from Ross Worner with a curling effort.
Hereford continued to struggle in the second half as the Shots closed things down. Rankine, who was a threat throughout, went close when he leaped above Michael Townsend to send a header just wide.
The Shots continued to look the more likely scorers and the second goal duly arrived nine minutes from the end.
Substitute Vincenti beat the Hereford defence to an Alex Rodman free-kick and headed into the corner of the net.
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