Southam went into this game off the back of an improved performance against Bromsgrove Sporting but although they battled hard, the elusive goals and points again did not materialise.
The deadlock was broken in the 18th minute when the lively George Brindley put in a telling cross which was slotted home from close range by Liam Rowley.
Southam responded well and it needed Perry Cotton to clear a free-kick from James Keller and then the follow up to protect Swifts’ slender lead.
The hosts were unlucky not to equalise in the 53rd minute after good work on the left wing from Joe Fisher. Dan Brierley’s resultant shot hit keeper Matt Hill’s head then the post and bounced dangerously across the six-yard box before a timely intervention from Swifts left-back Kyle Bache prevented a tap-in for the onrushing forwards.
From the resultant corner, Hill rose to push over a goalbound header from skipper Ben Nicholson.
Nicholson again came close from another corner a couple of minutes later with his flashing header going just wide with Hill beaten.
However, Swifts weathered the storm and began to exert pressure of their own.
A needlessly conceded foul allowed them to double their lead, Ryan Ball curling his free-kick around the wall to beat Harry Gardiner in the 67th minute.
Mick Bloore then forced the ball over the line to make it 3-0 to the visitors and there was still time for Ball to win and miss a penalty for the visitors.