Gremio's city rivals Internacional gave themselves a boost ahead of their visit to Libertadores Cup holders Estudiantes in La Plata in the quarter-finals on Thursday when they came back from two goals down to win 3-2 away to Goias.
Corinthians, looking to win the championship after their Libertadores Cup hopes in their centenary year were dashed by Flamengo, went ahead at the Olimpico in Porto Alegre after five minutes with a header by midfielder Ralf from a Dentinho corner.
Striker Souza, playing in place of Ronaldo, scored the second 20 minutes into the second half when he netted after a poor clearance by central defender Bruno Collaco.
Substitute Maylson pulled one back 10 minutes later but Corinthians defended their advantage to open a two-point lead in the standings.
"Against Gremio, who are a strong team, we got a very important victory ... It's a great merit to get a win in here," Corinthians' left back Roberto Carlos told reporters.
"It's not normal at Corinthians, in such an important year as this, to play only one competition, but destiny made that happen."
Inter, who beat Estudiantes 1-0 at home in last week's quarter-final first leg, rested some first team players and were 2-0 down at half time.
Striker Walter scored twice in the second half and was also fouled for the penalty eight minutes from time, which 19-year-old playmaker Giuliano converted for the win.
Champions Flamengo, upset 3-2 by Universidad de Chile in the home leg of their Libertadores tie, were held 1-1 by Vitoria on Saturday.
Sao Paulo, who upset Cruzeiro 2-0 away in an all-Brazilian Libertadores tie in midweek, lost 2-1 at home to Botafogo.
Cruzeiro, also resting several players, had to come from behind to draw 2-2 at home with Avai after having defender Leonardo Silva sent off in the 17th minute.
Striker Wellington scored twice in seven minutes in the second half including the equalising penalty on the hour after Avai goalkeeper Ze Carlos was sent off.
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