An early goal from Gary Teale calmed the nerves of the Owls and they looked comfortable enough in the first half but a spirited start to the second half saw the home side twice draw level only to see Wednesday strike back immediately.
The live ITV cameras were in attendance looking for a cup upset but a professional performance saw Wednesday progress and earn a second round home tie against Northampton Town.
Former Eire international striker Clinton Morrison was given the man-of-the-match award and his clinical display in front of goal underlined the visitors’ superior quality.
Morrison set up the first with a clever ball across the box allowing Teale a tap in and in the second half his shot on the turn came back off the upright for Mellor to tap in Wednesday’s second goal.
The former Crystal Palace front man then rounded the Southport goalkeeper to put the Owls in front for a third time and moments later he gave his side breathing space by adding a fourth with a low strike into the corner on the turn.
Morrison joined the Owls on a free transfer in the summer and was seen as a high-profile signing for the League One side as they looked to rebuild a squad capable of challenging for promotion following their relegation from the Championship.
A goal on his debut in a 2-0 win over Dagenham & Redbridge on the opening game of the season got his Owls career off to the perfect start but prior to the Southport game he had only scored twice for the club and had not found the net since August.
Regardless of the standard of the opposition, strikers thrive on confidence and his two goals, combined with a good all round display will hopefully give him the filip to kick on and show his quality on a regular basis as Wednesday attempt to reignite their promotion challenge.
Disclaimer: The views in this article are that of the writer and may not replicate those of the Professional Footballers' Association.