The Hoops were the better side for the opening half an hour, with a Jayden Carbon effort causing a problem for visiting goalkeeper Chris Renshaw, while Josh Parker had a header caught.
Southport improved in the final quarter of an hour of the first half though, with Danny Lloyd flicking an unchallenged header wide.
City took the lead though five minutes into the second period, as Parker raced to the byline and teed up Jacob Roddy, who had plenty to do as the ball bounced up in front of him, but the 21-year-old demonstrated superb technique to smash a strike past Renshaw.
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The Hoops had a few warnings sent their way via set pieces, and it was through the aerial route that Southport found an equaliser.
Just after the hour mark, a deep ball into the penalty area was headed goalwards by Danny Philliskirk.
Kai McKenzie-Lyle did well to dive to his left and push the ball away, but Philliskirk also reacted quickly, and was in the right place to place the ball into the back of the empty net.
City needed McKenzie-Lyle to make an almost identical save a few minutes later, and this time, there was nobody following up for Southport.
The Hoops are 19th in National League North, three points above the bottom four.
Ross Jenkins’ side make the trip to sixth-placed Hereford on Tuesday night.