Asfordby went into the game on the back of five straight wins and having already sent their local rivals out of the President’s Cup earlier in the season.
Both sides started slowly, but Asfordby made an early substitution, bringing on Callow who quickly helped to settle the midfield. He combined well with Henshaw-Cox and Felstead to free Atherley who was felled, but the penalty appeals were waved away.
Foxes hit back with Shaun Smith firing high and wide when he looked a likely scorer before Marcus Rowlands cut inside and sent a fierce drive over the bar.
Asfordby were growing in confidence with new signing Watson and Foxes old boy Jones going close, while Foxes keeper Lovegrove somehow pushed a goalbound shot onto the bar before Frazer Lewis cleared.
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Another run by Rowlands opened up the visitors, but his fierce low cross flashed across the face of the goal, and Smith headed straight at the keeper from close range.
Asfordby hit back after half-time and Lovegrove had to move smartly to keep out a low shot from the edge of the area, before Lomas sent in a superb cross only for Smith to lose his footing.
The visitors had three gilt-edged chances to take the lead. Watson beat three men ,but couldn’t find the goal, and minutes later Atherley’s fine run and shot was saved before Felstead volleyed Jones’s fantastic cross well over.
But Melton went ahead when Asfordby keeper Leatherland was unable to gather Lomas’ corner cleanly and substitute Tom Dryell scored with a sweet half-volley.
Yet from the kick-off Asfordby went straight up the other end and Herbert’s superb low shot to equalise.
In extra time both teams had chances to take the lead, but another good incisive move from the Foxes ended with Adam Lomas driving them in front after good work from Rowlands.
The Foxes this time had a penalty appeal turned down when Smith went down in the area, and Asfordby went close when Alex Kotarba headed a corner against his own bar.
Rowlands flashed a shot across the face of the goal, but with eight minutes left Asfordby gambled, taking off defender Skinner, who had run himself into the ground, to add a fourth attacker.
This paid immediate dividends when Watson raced clear to claim his second goal in two games to force penalties.
Both sides converted their first five penalties to take it into sudden death, and when Leatherland saved the Foxes’ seventh penalty, Sharp, in his 12th season with the club, sent Asfordby into the quarter-finals.
Foxes: C. Lovegrove, J. Dawkins, G. Wilkinson, F. Lewis, A. Lomas, L. Thorpe, R. Gavin, C. Ainge, S. Smith, M. Rowland, B. Carroll, A. Kotarba, T. Dryell, A. Horobin.
Asfordby: Atherley (c), Callow, Jones, Wesson, Skinner, Reed, Felstead, Watson, Kahlon, Leatherland, Richards, O’Neil, Herbert, Henshaw-Cox, Sharp.