Former Fenerbahce playmaker Alex, 35, scored both goals in Coritiba's win on Sunday as Sao Paulo, who won the championship three times in a row between 2006 and 2008, reached the halfway point in 18th place with 18 points.
Alex snapped up a rebound in the 32nd minute after goalkeeper Rogerio Ceni parried Vitor Junior's shot, then curled in a free kick in first-half stoppage time.
Levi Gomes, previously assistant coach, took over at Nautico to replace Jorginho, who quit after five matches on Thursday, and watched his team grab an unexpected point at Corinthians.
Alexandre Gallo, Vagner Mancini, Silas, Ze Teodoro and Jorginho have previously occupied the hot seat this year at Nautico, who remained bottom of the 20-team table with nine points.
Cruzeiro reached the halfway point with 40 points and a four-point lead over Botafogo at the top after Ricardo Goulart's second half goal gave them a 1-0 win over Flamengo.
Flamengo, under former Brazil coach Mano Menezes, are a modest 15th with 22 points, only three clear of the relegation zone.