Lincoln recorded their first win under Gary Simpson thanks to Alan Power's first-half penalty against Southport.
Power scored after Aaron Chalmers fouled Jamie Taylor in the area.
Southport had a great chance to level when Paul Farman fouled Shaun Whalley in the box, but the keeper redeemed himself by saving Whalley's spot-kick.
Both sides ended the game with 10-men after Imps striker Vadaine Oliver and visiting defender Neill Byrne saw red for an off-the-ball incident.
VIEW FROM THE DRESSING ROOM
Lincoln City manager Gary Simpson told BBC Radio Lincolnshire:
"We had to stand up to them and to keep a clean sheet was tremendous. I thought we got a good shift out of everybody. We're not in a good position so that's what we're going to need.
"We might not have as much ability as one or two teams in the division but we can give our all and that's what we did today.
"I thought the back four were tremendous, they were solid and the two in front of them were solid but from there we tried to be more attacking because we were at home.
"I'd watched Southport and I knew they were big and strong and good from set plays so it was a case of finding our character, our strength and our desire."