The victory left Flamengo, winners for the fifth time since the championship was instituted in 1971, two points clear of Internacional and outgoing champions Sao Paulo, who also won their final matches in a thrilling run-in.
Flamengo completed the 38-match campaign with 67 points. Inter and Sao Paulo, who beat relegated Santo Andre and Sport Recife respectively, both finished with 65.
Brazil striker Adriano failed to find the net for Flamengo on Sunday but ended the championship as joint top scorer with 19 goals alongside Atletico Mineiro's Diego Tardelli.
Cruzeiro, Libertadores Cup runners-up this year, grabbed fourth place and the last ticket to South America's top club competition in 2010 with a 2-1 win over Santos.
With Inter, who beat Santo Andre 4-1, set to snatch the title if Flamengo were held to a draw, Angelim headed the decisive goal in the 70th minute from Serbian Dejan Petkovic's corner to unleash wild celebrations on the Maracana terraces.
"This is a dream for me as a fan and player of Flamengo. I have to thank Pet (Petkovic) who sent over a marvellous ball for my goal," said Angelim, surrounded by supporters who invaded the pitch to celebrate after the final whistle.
Fluminense, Flamengo's big Rio de Janeiro rivals, escaped relegation with a 1-1 draw away to Coritiba, finishing with an unbeaten run of 11 matches including seven wins.
