Violence in big cities, including football hooliganism, is one of the big problems Brazil faces two years before staging the World Cup finals.
Police reported that about 500 Palmeiras fans were being escorted to the municipal Pacaembu stadium where Corinthians play when some home supporters confronted them with firearms, iron bars and home-made grenades.
Five people were hurt including the 21-year-old fan, who was shot and died later in hospital.
Film footage by amateur witnesses broadcast on television showed scenes of a street battle and a fan lying on the ground bleeding and waiting for assistance, which he was given by police after the fighting before being taken to hospital.
Media reports said no one was arrested.
"The military police were caught between the two gangs but for an hour people's lives were in danger," police corporal Adriano Lopomo told TV reporters.
"The military police had no way out unless it was to retreat and practically help the conflict."
The scene of the battle is an area where there are often confrontations between rival fans of the big Sao Paulo clubs.
Since police have managed to all but end the violence within the stadiums, fighting has moved into the surrounding areas.
Last year, a Corinthians supporter was killed by Palmeiras hooligans.
On Sunday, there were also scuffles between Corinthians fans and police at the stadium's main entrance minutes before kick-off.
TV footage showed people who were still outside when the game was about to start trying to force their way in. Mounted police used tear gas to push the crowd back.
Corinthians won the match 2-1, ending Palmeiras' 21-match unbeaten run.
