Southport claimed their fifth away league win of the season, courtesy of a first-half own goal by Nuneaton defender Stephen O'Halloran.
The game's only goal came on 15 minutes as O'Halloran turned the ball past his own keeper from the edge of the area.
The hosts had a good chance to take the lead on 55 minutes when James Armson's shot from the left edge of the area was well saved by Tony McMillan.
Relegation-threatened Boro finished strongly but Southport held on.
VIEWS FROM THE DRESSING ROOM
Southport manager Liam Watson told BBC Radio Merseyside:
"In the first half, we were the better side. We had the break with the goal and that was probably the only bit of quality when we got in behind them.
"We were very strong defensively and we should have had two or thre later on. We had some great chances.
"It's our first clean sheet for a long time so we'd have taken that."