The violence erupted among a group of African men near the Austral Hotel in Bent St, between Rundle and Grenfell streets, just after midnight.
Two other African men were treated for "minor" stab wounds and "numerous" knives, tyre levers and wooden clubs were found in the street.
Police say the brawl was the culmination of a string of confrontations between African men since Friday night.
Dozens of interstate people had come to Adelaide for a "Miss Africa" pageant held at Norwood and many were involved in "a handful" of fights, police said.
Officers responded to a fight outside a Hindley St nightclub on Saturday morning when about 150 people were arguing, but a spokesman said he was not aware if anybody was arrested.
After last night's brawl, a Marden man, 21, and a Murray Bridge man, 19, underwent emergency surgery for serious torso wounds, while an Ingle Farm man, 19, and a Kilburn man, 20, were treated for arm or back lacerations.
Police officers who were leaving after their shift this morning from the station at the corner of Bent and Grenfell streets - about 100m away from the brawl - ran to the scene and called for back-up to quell the violence .
Their quick action prevented further injuries, Detective Chief Inspector John Gerlach said.
"It was certainly the case (that) had we not responded so quickly, there would have been further injuries," he said.
Chief-Insp Gerlach said some of those involved in the fight had been at the Austral Hotel before the brawl erupted.
"This incident occurred in the street, it did not happen in the nightclub," he said. "From what we see now, there's no doubt some people have armed themselves in the event they came together again or they might have been looking for trouble.
"We can see now in hindsight that that's probably what's occurred."
Two men underwent surgery early this morning for serious stab wounds. Another two men suffered minor stab wounds.
Police have charged a Victorian man, 20, with aggravated causing serious harm and fighting. A Kilburn man, 19, a Victorian man, 21, and a West Australian man, 22, were charged with behavioural and weapons offences.