
United chucked away a two-goal lead inside nine minutes through a Dominic Roma own goal and Jake Wright, with Gregg Smith and Anthony Dwyer forcing extra-time.
Luther Munakandafa’s strike was cancelled out by a Scott Pollock penalty, on a night which also saw the Pilgrims hit by three injuries.
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It was the visitors who kept the never best as they secured a 4-2 shootout win to book a trip to Solihull Moors.
Boston host Hereford United at the weekend as they return to National League North action.