The Wongers came back from behind to edge out their local rivals 3-2, who finished the game with
eight players on the pitch.
Second half red cards for Danny Stevens and Alex Aldrich were followed by another Louth player being sin-binned late in the game.
Louth took an early lead through an excellent volley from Ellis Barker.
Horncastle replied with an Andrew Bullivant penalty before the interval.
Another spot kick by the same player gave Horncastle the edge before Stevens received his marching orders.
From the resultant free kick Bullivant completed his hat-trick.
Louth pulled a goal back, but suffered another set back when Aldrich was sent for an early shower.
They were left with eight players on the pitch when the referee sin-binned one of their strikers.
The visitors piled on the pressure in a bid to send the tie into extra time, but Horncastle’s defence
held firm to secure their passage into the last four.