The West Midlands Regional League visitors had the first clear scoring opportunity in the eighth minute, winger James Baldwin shooting weakly at Tom Cross.
Southam skipper Louis Bridges then completely missed a delicious ball swung in by Mitch Piggon when it looked easier to score.
He was to make amends in the 22nd minute, however, cutting inside a defender before curling a shot into the far top corner.
Cross was called on to save with his legs in the final minute of the half and the visitors remained on the front foot after the break.
They got back on terms in the 54th minute through Danny Crudgington after the home defence collectively lost concentration and scored a second 20 minutes later courtesy of Tom Piggot following another defensive error.
Not even a second booking and subsequent red card for Ross Love disrupted Gornal as they easily coped with the home side’s disjointed efforts.
Indeed, the ten men might have scored a third a minute from time as Piggot ran through the Saints defence only to be thwarted at the last by Cross.
Southam make successive away trips to Pilkington XXX tomorrow and Littleton on Wednesday in the league.
Southam Reserves produced a polished second-half performance to beat Alcester Town Reserves 4-1 in the first round of the Nursing Cup.
Sukki Nijjar (2), Steve Thomas and Kurt Parsons scored the goals.