This was due to a 3-2 defeat at A.F.C. Queensway - one of the other sides chasing higher grade football next season.
The Brigg team's scorers were Sol Hari and Joe Stothard.
Briggensians - who have three games to play - are now third in the table behind runaway leaders Shape Changers and Queensway.
Barnetby United, who are third in division one, enjoyed an 8-0 home win against Bottesford Town Reserves yesterday.
Leading scorer Cameron Hill banged in five, with the other goals coming from Andy Dawson, Ryan Lidgett and Will Hartley.
Saturday, March 18 (3pm KO)
Division One: Barnetby United v Limestone Rangers (referee A Farr)
Division Three: No game for Briggensians or for Barnetby United Reserves, who are fourth in the standings.