Report from BBC Sport
Osayamen Osawe scored a second-half winner to take Southport out of the Conference Premier relegation zone.
Osawe, who had earlier missed a great chance, punished a defensive mix-up between Paul Bignot and Shaun Pearson.
Lenell John-Lewis had put play-off chasing Grimsby ahead in the ninth minute from Ross Hannah’s cross.
Scott Brown levelled in the 36th minute from 25 yards before Hannah hit the inside of the post, while at the other end Pearson twice hit the bar.