Boro took on Chesham United at Liberty Way in front of a crowd of 1,379 and fell behind to a Burnell goal in the 45th minute.
Foster equalised in the 66th minute and the match appeared to be heading for extra time before Marsden set up a final against Chasetown with an 86th minute goal.
Atherstone hosted Chasetown but trailed to a Batchelor goal after 26 minutes. A minute later, Perrow added a second and then a third after fifty minutes.
Birch scored a fourth in the 64th minute before Perrow completed his hat-trick and made it 5-0 to Chastetown a minute later.
In the Midland Combination Premier Division, Massey Ferguson were beaten 2-0 at home by Pershore Town.