Mark Shelton's first-half strike proved enough for Salford as they hung on to beat Grimsby 1-0.
The Mariners almost levelled in stoppage time when Luke Waterfall's shot was brilliantly saved by Salford goalkeeper Kyle Letheren as the hosts secured their first win since the opening day.
Grimsby almost struck early on when Letheren produced a superb save to keep out Matt Green's header.
Green then went close with a strike from 20 yards, while at the other end Adam Rooney headed narrowly over the top.
The hosts scored in the 21st minute when Shelton's well-struck 25-yard free-kick took a deflection off the wall before beating wrong-footed Grimsby goalkeeper James McKeown.
Elliott Whitehouse saw a shot blocked as Grimsby pressed for a leveller before the interval.
Town thought they had equalised four minutes after the restart when Jordan Cook curled home a sweet free-kick, but referee Chris Sarginson eventually reversed his decision and awarded the free-kick to Salford.
Salford replied with Cameron Burgess glancing a header just off target as he met Shelton's cross.