The Lanarkshire side went through on penalties after the sides drew 2-2 in their third round replay at Newtown.
But United are to protest after referee Chris Graham wrongly played a period of extra-time despite the competition rules stating the tie should have gone straight to penalties.
Despite being told by both sets of club officials, and shown the rules, he ignored protests and bizarrely went ahead and played one period of extra time before taking the game to penalties which were taken in darkness.
In the game itself, Bo’ness miswsed a host of chances including a first half penalty when Ruari MacLennan’s effort was brilliantly saved by Blantyre keeper Law.
Nicky Hogarth: Former Graeme High pupil signs for Falkirk on loan from Premier League newcomers Nottingham Forest
McGuffie talks style of play and mentality ahead of Peterhead clash
Falkirk set to bring in goalkeeper ahead of Peterhead match
Syngenta: Finlay could be playing 'four or five' levels above the EoS second division, says boss
'I'll be ringing the changes' says Stenhousemuir boss Swift ahead of Stirling Ablion trip
Blantyre went ahead immediately after the interval when Jordan O’Donnell picked out Martin McLaughlin who fired low into the corner.
With anxiety levels rising United got back on level terms on 76 minutes through a fantastic Ross Campbell header from a Robert Sloan cross.
United then won a corner after Keast had seen his shot brilliantly saved and from the set piece Keast got on the end of the Marty Wright corner to give Bo’ness the lead.
The hosts then missed chances to seal it and in injury time Kierin Coleman headed in the equaliser that should have meant penalties.
During the one half of extra time nothing of note happened other than more protests that were ignored and after a lengthy delay with it becoming pretty dark the game went to penalties.
Sloan, Wright and Ruari MacLennan scored with Keast, Will Snowdon and Campbell missing. Gary Campbell netted the winner for Blantyre and Bo’ness will rue the missed opportunities in the two matches.
Unless Bo’ness have their protest upheld Blanture Vics will now go on face Linlithgow Rose - 5-0 winners at Dundee North End - in the fourth round.