Mike West’s clever flick from close range gave the hosts a 24th minute lead but 7 minutes later, the hosts were reduced to ten-men as Craig Braham-Barrett received two yellow cards in 4 minutes.
The first was for simulation when he was tripped inside the area, and then he received a second yellow for deliberate handball on the goalline.
Daniel Green duly stepped up to convert the resulting penalty for the Stones, winners of the competition back in 1985, driving a low shot to right of Sam Beasant.
Abobaker Eisa put the Stones ahead early in the second half when he controlled a sharp cross before netting from close range.
Kevin Davies won`t be managing at Wembley this season either as his Southport side were comprehensively beaten 3-0 at the Merseyrail Community Stadium by National League North rivals Stockport County.
The visitors` fans went into the replay with hopes not particularly high, despite recent good league form, as they hadn`t won at Southport since 1957!
Southport impressed in the original tie at Edgeley Park last weekend, but once Jason Oswell`s opener went in after 18 minutes when he got on the end of a Matty Warburton through ball, there only looked to be one winner.
County doubled their advantage just past the half-hour mark when Warburton was brought down by recent Port recruit, Steve Howson, and Warburton got up to send home `keeper Jon Worsnop the wrong way from the penalty spot.
County had several opportunities to increase their lead, but it wasn`t until the 65th minute that they were able to completely relax when, following a Southport corner, the home side broke away with Worsnop parrying a shot from James Ball before Warburton netted the rebound to make it 3-0.
Stockport are away to Evo-Stik League Premier side Lancaster City on 16th December.