In their final Division One match of the season, Old Boys found themselves 4-0 down at the break to goals from Jamie Rowbotham, Lewis Farman, Alex Otter and Ricky White.
No further damage was done in the second half as Tetney made it 15 wins from 16 matches to remain two points behind leaders North Somercotes with a game in hand.
Louth lie in fifth place, but are likely to be leapfrogged by sixth-placed Holton Le Clay who have five games in hand.
Their league campaign may be over, but Old Boys still have a two-legged Cusworth Cup tie to come against Grimsby Borough Development on Saturdays, March 23 and 30.
Alford Town ended their Division Two season in fourth place after an encouraging 3-3 draw with champions Susie Star on Saturday.
The visitors led 1-0 at the break, but Town fought back to earn a share of the spoils through Jess Marshall, Andi Reeson, and Alex Simpson.
Louth Old Boys Reds, meanwhile, made it into the final of the East Lincs Cup as they fought back for an aggregate win in their semi-final.
The Reds trailed 3-2 going into the weekend’s second leg at North Cotes, but goals from Jordan Tebbs, Ottis Whittleton and Bailey Wright gave them a 3-1 win and took them through, 5-4 on aggregate.
In the final they will meet the winners of Sutton Rovers and Susie Star.
Having finished fourth in Division Three the previous week, Louth Old Boys Vets stormed past Alford Town Reserves in the Tom Sandys Trophy.
They thrashed Alford 6-1 to go second in Group A, six points behind leaders North Somercotes with a game in hand.