Police fired tear gas as the brawlers lit firecrackers and tried to tear down fencing separating the stands from the field.
Eighteen people were stabbed during the melee, said Manuel Infante, spokesman for Cali's Emergency Prevention Committee. They were treated at the stadium and taken to a local hospital. Another 60 suffered bruises and other minor injuries.
A young pregnant woman and three police officers were among the wounded, the Red Cross said.
Tensions flared over referee Wilman Roldan's decision not to call a penalty kick against Cali. America protested the no-call, players traded blows on the field and America coach Diego Edison Umana got into the fray, elbowing his Cali counterpart Daniel Carreno.
Cali Mayor Jorge Ivan Ospina called Umana "directly responsible" for the violence and said the stadium's stands would be closed temporarily.
Umana had harsh words for the refereeing later in comments published on the Web site of El Tiempo newspaper, but said there was "no excuse" for his behavior.
"It's my fault, and if I have to leave soccer I'll go," Umana said.
Fans of the two Cali squads have had frequent clashes in the past, though less serious.
"This cannot happen again," vowed Juan Carlos Abadia, governor of Del Valle department.
The chaos led Roldan to whistle an early end to the match, which Deportivo won 1-0 on a goal from defender Freddy Hurtado.