Although end-to-end, the first half failed to spark into action, with both teams seemingly unsettled, only creating half-chances in their attempts to break the deadlock.
The first goalmouth action came after 12 minutes when Ryan Crockford's inswinging corner took a deflection, with Steve Pickford clearing off the line at the back post.
Southport's best chances came from Liam Blakeman who seemed to be the hosts' most dominant threat against the resolute Aldershot defence. The best chance fell just shy of the half-time whistle when his 20-yard goalbound shot was well-saved by Nikki Bull.
Aldershot came out in the second half with a touch more determination to get the advantage with Jonny Dixon seeing his shot go slightly over the target, and Ryan Williams forced Dickinson to save well with his feet.
On the hour mark, Robbie Booth nearly broke the deadlock when he latched onto a right-wing free-kick from Jerome Fitzgerald, but he saw his effort come back off the post.
The deadlock was broken thanks to a controversial decision when Michael Powell was adjudged to have fouled Kirk Hudson just inside the 18-yard box, with Barnard coolly slotting the ball to his left, with Dickinson going the wrong way.
Southport tried for an equaliser with Neil Robinson hitting the post with an 18-yard shot, while Booth's shot from the rebound going high into the park behind the ground.
Despite the late flurry, Southport could not equalise, as they said goodbye to their part-time status, as their future in the Conference beholds full-time football.