Boston Town are out of the United Counties League Knockout Cup
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Liam Adams was unlucky to see his free-kick from 25 yards hit the cross bar in the first half. Just before the break, the hosts took the lead - and then doubled their advantage 10 minutes into the second half.
Lutterworth were then reduced to 10 men and with 7 minutes to go Balint reduced the arrears with his first goal for Boston Town.
The home side restored their two goal cushion two minutes later but Balint pounced again right at the death to leave the final score 3-2.
Jordan Nuttell had earlier had his goal ruled out for offside.
The Poachers haven't made it past the 2nd round since 2016.