This time it was promotion pushers Stalybridge Celtic at their Bower Fold home, to ensure four wins out of four for the Sandgrounders.
Liam Watson's team cemented their position at the top of the table through a lone goal from Tony Gray.
But it was visitors' defence who deserved most praise, with Earl Davis and James Connolly solid in the middle, and Kevin Lee and Chris Lever dominant down their flanks.
The challenge from the hosts came from the kick-off as Chris Williams stabbed a low danger ball to Lee Ellington, but the ball was guided by Davis for Tony McMillan to pounce.
Minutes later, Steve Torpey's free-kick was sliced into the air by Lee, with the Southport keeper scrambling back to punch the ball over.
Williams created space for himself, but shot over from 20 yards, and Southport delivered a sucker punch.
The Celtic defence were slow to stop Lee's right-wing cross to Gray, who turned to face goal and almost in slow motion it seemed was clear to bury into the bottom-left corner, with the keeper a mere observer.
Southport were able to sit on their lead for the rest of the half, the only other chance was from a Matty McGinn corner which went through to James Connolly, but his header glanced over.
Buoyed on by Watson's half-time thoughts, Port came out with renewed vigour, and Paul Sykes nearly gifted a second as his horrendous back-pass to his keeper went through to Gray, who took the ball around Phillips, but his shot was stopped by a comination of two covering defenders who had scrambled back to the line.
The rebound landed with Ciaran Kilheeney, whose shot went back to Michael Powell, who was just unable to guide his shot under the bar from the edge of the area.
Celtic were reduced to speculative shots, Keith Briggs going closest, but Port were a danger on the break, especially Mark Duffy, who got the ball out to Kilheeney on the right, and he timed his pass to perfection for Gray, but the striker shot into the side netting.