The Saints were 3-1 winners but had to come from behind after going an early goal down.
It was Huntingdon’s Declan Rogers who scored first, on 14 minutes, lobbing debutant goalkeeper Jack Mitchell after a swift counter-attack which had begun with a Dan Jacob shot hitting a post.
Chris Manangu, also making his full debut after coming on as a substitute at North Greenford last month, equalised on 36 minutes, picking his spot sweetly, before Pearson Mwanyongo found Jacob for St Neots’ second two minutes later.
Saints manager Dennis Greene sent on Stefan Moore and Lewis Webb in the second half and shuffled his pack but it was Huntingdon who went close shortly after the restart, Ondre Odain breaking through the home side’s defence but shooting wide.
A brilliant 60-yard Lewis Hilliard pass fed Moore for the Saints’ third, before the striker clipped a post late on.
St Neots will now face either St Ives Town or Yaxley in the semi-finals.
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