Stamford slipped to third in the table with a 2-1 defeat at promotion rivals King’s Lynn on New Year’s Day.
The Daniels went ahead through an Andy Hall strike early in the second half but Shane Tolley pulled the hosts level with quarter of an hour remaining and then secured them all three points with an 87th minute winner.
Stamford are now one point behind second-placed Sutton Coldfield, albeit with four games in hand, but they trail leaders Coalville Town by 11 points.
The Daniels next match is at fifth-placed Gresley on Saturday.
Evo-Stik League First Division South results:
Belper Town 2-0 Mickleover Sports
Gresley 1-2 Coalville Town
Halesowen Town 1-1 Chasetown
Kidsgrove Athletic 1-4 Sheffield FC
Kings Lynn Town 2-1 Stamford
Lincoln United 1-0 Brigg Town
Loughborough Dynamo 13-0 Hucknall Town
Newcastle Town 0-1 Market Drayton Town
Northwich Victoria 4-3 Leek Town
Rainworth Miners Welfare 2-0 Carlton Town
Romulus 1-1 Sutton Coldfield Town