Only one place and two points separated the Louth side and their cup final opponents Cleethorpes Town A in East Lincs Combination Division One, and a tight final was expected.
After a goalless first half, Johnson came off the bench to grab the winner.
Clubmates Louth Old Boys Reds could make it a cup double next week when they line up against North Somercotes United Reserves in the Tom Sandys Trophy final next Wednesday at Fulstow (ko 6.20pm).
The Reds warmed up with a 5-0 win over Marsh Rovers in the group stages of the Tim Sales Trophy, Bailey Wright with a brace, and Tom Petchell, Wayne Russell and Jordan Tebbs with the other goals.
But there were group match defeats for Louth OB Vets who went down 5-2 at home to AFC Grainthorpe, and Alford Town Reserves who lost 2-0 at home to North Somercotes.
Sutton Rovers restored some pride after winning the second leg of their Cusworth Cup tie 4-2 against Tetney Rovers, having lost the first leg 13-1.