A drab first-half saw little goal threat at either end despite the Welsh side dominating proceedings.
In a brighter second period, Wrexham goalkeeper Shwan Jalal pulled off good saves from two Andrai Jones' headers.
The hosts took all three points when right-back Edwards sneaked in to force home a cross from Paul Rutherford on 88 minutes.
Wrexham manager Dean Keates told BBC Radio Wales:  "It was the perfect result. Performance-wise it was not where we wanted to be, but I would say it was all about getting the result today not about the performance.
"They worked hard, it was a bit scrappy, a bit nervy. But we got the goal and it was all about the three points in the end."
Match ends, Wrexham 1, Southport 0.
Rob Evans (Wrexham) is shown the yellow card for a bad foul.
Second Half ends, Wrexham 1, Southport 0.
Goal!  Wrexham 1, Southport 0. Kai Edwards (Wrexham).
Substitution, Wrexham. George Harry replaces Jordan White.
John Rooney (Wrexham) is shown the yellow card for a bad foul.
Substitution, Southport. James Caton replaces Ben McKenna.
Second Half begins Wrexham 0, Southport 0.
First Half ends, Wrexham 0, Southport 0.
First Half begins.
Lineups are announced and players are warming up.
A late goal from Kai Edwards gave Wrexham a first win in four National League games as they saw off Southport.