Old Boys needed spot-kicks to see off Grimsby Borough Development B after a seesaw Town Trophy tie at London Road.
They trailed 1-0 at half-time, but levelled in the second half to force extra time, and both sides scored again to send the tie to a shoot-out which Louth won 4-1.
Ellis Barker and captain Aron Burton were on target for Louth before the shootout, while Robert Hodgekins was shown a straight red card.
The Louth side will face either AFC Louth or Immingham Town Reserves in the semi-finals.
It was also a good day for Louth Old Boys Reds as they went third in Division Two with a 5-1 rout of Alford Town.
The teams were locked at 1-1 at half-time with Jordan Tebbs on target for the Reds and James Cole getting Alford’s goal.
But Tebbs ran riot in the second half, scoring four more to take his season’s goal tally to 15 as Alford dropped two places to fifth.
Elsewhere in the division, AFC Louth claimed their first points of the season without kicking a ball as hosts Chapel Swifts conceded their match.
Division Three side Alford Town Reserves went out of the Town Trophy with a 3-1 defeat at home to Marsh Rovers, Lee Twigg with the consolation.
Fixtures – Division One (1.45pm): Louth Old Boys v North Thoresby.
Division Two (1.45pm): Louth Old Boys Reds v North Cotes.
Division Three (1.45pm): Barnoldby v Louth Old Boys Vets; Burgh Athletic v Alford Town Res.
Junior Challenge Cup round two (1.30pm): Sutton Rovers v Alford Town.
Town Trophy quarter-final (1.30pm): AFC Louth v Immingham Town Res.