Ali Cope finished off a great team move after 30 minutes to give White Horse the lead and, despite Riccall throwing everything bar the kitchen sink at their division one opponents, they were unable to break through to grab an equaliser.
Jon James then added a second and decisive goal for Huntington which proved to be enough to put them into the quarter-final draw.
In the league, the focus switched to the bottom half of the premier division table with three sides having an opportunity to pull clear of relegation favourites York St John University.
Easingwold made the most of the chance, putting five past Aviva. Dave Adams and Simon Webster gave Town a 2-0 half-time lead before Steve Aconley made it 3-0 shortly after the restart.
Warren Lowe gave Aviva a glimmer of hope but Jordan Grose and John Dey finished the scoring.
Grasshoppers pressed from the first whistle and, despite resilient Poppleton defending, they broke through on 22 minutes when Dale Holding ran 70 yards to drill his finish into the roof of the net.
A handball then gave Wiggy goalkeeper Michael Clancy the chance to double the lead from the spot. Lee Stewart added a third with 20 minutes to go.
In division one, Total Sports United orchestrated a major upset as they defeated promotion-chasing Osbaldwick 2-0. Ben Brannigan gave Sports the lead at the interval, with Richard Walton adding their second late on. Total Sports now need one more victory from their remaining three games to be certain of avoiding relegation.
Pocklington snatched a vital point at home to Tockwith thanks to Chris Murray’s equaliser.
• Don’t miss The Press tomorrow for more league reports.