It wasn't until the final four minutes, though, that Accrington made their superiority tell against a Southport team supposedly boosted by three loan debutants.
The Lancastrians bossed the game from first whistle to last with Romauld Boco in outstanding form. The Benin international scored his first Conference goal but had enough chances to finish with a double hat-trick.
When he finally limped out of the match with 15 minutes left, replacement Andy Mangan netted a late goal as did captain Paul Mullin.
Those final two strikes gave the final scoreline a truer picture of Accrington's dominance.
Southport managed just one shot on target, but Adriano Rigoglioso's first half effort hardly troubled keeper Darren Randolph. Indeed, Randolph, who now returns to Charlton, couldn't have had a quieter afternoon throughout his loan spell.
The Sandgrounders, who had four players cautioned including newcomer Chris Brass, didn't win their first corner until the 82nd minute, while substitute Kevin Lynch had the visitors'best chance in the second period.
Accrington had to wait until the 31st minute to take a deserved lead, Leam Richardson and Gary Roberts setting up Ian Craney. But almost immediately Stanley doubled their advantage as Boco charged into the area past Earl Davis before firing home.
That's the way it stayed despite many chances until Stanley's final flourish rounded off a dazzling display.