Stamford came back from two goals down in sensational style to make it four wins from four games away from home this season.
The Daniels were trailing to goals from Adam Lee and Liam Davis at Brigg but pulled off a stunning turnaround.
Gary King pulled a goal back in the 70th minute, Greg Smith levelled two minutes later, and just two minutes after that Andy Hall converted a penalty to put the Daniels ahead.
The victory leaves Stamford in fourth place, behind Coalville, King's Lynn and Sheffield but with games in hand of the trio above them in the Evo-Stik League First Division South.
Stamford's next match is at Hucknall on Tuesday evening.
Results: Brigg 2-3 Stamford; Halesowen 2-3 Sheffield; Hucknall 3-2 Chasetown; King's Lynn 3-0 Romulus; Loughborough 0-0 Belper; Mickleover 2-2 Market Drayton; Newcastle 2-2 Lincoln Utd; Rainworth 3-1 Kidsgrove; Sutton Coldfield 0-4 Coalville.