Rexham made progress in hunting to automatically raised from the first round on Saturday when 1-0 out of 10 players Stockport County finished second.
Rexham has asked for a third consecutive request this season, and Jay Rodriguez’s first-half strike was enough to get all three points and continue the battle to a place in the tournament.
Wales were shot before Ibo Tolay was sanctioned by a handball. Rodriguez took the penalty shootout and saw his attempt by goalkeeper Kori Adai, although the striker scored the first goal for the club since joining the club in January.
Stockport was not pushing a equality, close to coming when Clum Cologne’s head forced Arthur Oconko in Rexham to save it, but couldn’t find it. Things were from bad to worse to Stockport when they were given a second yellow card in 81 minutes.
Rexham will face a close task to the top of the lead at Birmingham City, who have nine points and two games. The best chance of success will be through second place.
Wicomb Wanderes, who are third on three points, are three points behind Rexham.