The title also gives the Sao Paulo club a spot in next year's Copa Libertadores, along with their main rival, current champions Corinthians.
Palmeiras won the tournament unbeaten in 11 matches. Coritiba opened the scoring with a free kick by Ayrton in the 62nd minute, but striker Betinho equalized just four minutes later with a header, putting Luiz Felipe Scolari's team in command.
Coritiba defender Pereira was sent off in the final minutes with a second yellow card. It was Palmeiras' first major trophy since the 1999 Copa Libertadores, and its 10th national title, one more than Santos. Palmeiras has also won eight national league titles and lifted another Brazilian Cup trophy in 1998.
Both the Copa Libertadores and the 1998 Brazilian Cup titles came in Scolari's previous stint at the club, before he led Brazil to the 2002 World Cup title and then coached Portugal and Chelsea.
It was the coach's fourth Brazilian Cup title. He had also won it with Gremio in 1994 and minnow Criciuma in 1991, when he first appeared in the national scene.
"This puts Palmeiras on the map again after a decade of struggles," Scolari said. "Now it's on the right path again."
Scolari has already said he will leave the club when his contract expires at the end of the year and is likely to coach a national team during the 2014 World Cup in Brazil.
Coritiba, the 1985 Brazilian league champion, was trying to win its first Brazilian Cup. It had been runner-up to Vasco da Gama last year, when it lost the decisive match at home 3-2 after a 1-0 loss in Rio de Janeiro.
One Palmeiras' top players in the title campaign is former Real Betis and AS Roma midfielder Marcos Assuncao, whose free kick cross led to Betinho's goal on Wednesday at the Couto Pereira stadium.
Betinho replaced Argentine striker Hernan Barcos, one of the team's top signings who was sidelined from both legs of the final because of an emergency appendectomy just hours before the first leg in Sao Paulo.
Chilean playmaker Jorge Valdivia scored Palmeiras' first goal in the match in Sao Paulo, converting a penalty kick before being sent off with two yellow cards, one of them for faking to throw a ball at an opponent's face.