Meanwhile, Botafogo debutant Hyuri provided the highlight of Thursday night's Brazilian championship matches by scoring a stunning individual goal in a 3-1 win over Coritiba.
Jorginho, who lost all five games in charge, became the fifth coach this year to part company with Nautico who are bottom of the Brazilian championship.
He made his decision immediately after seeing his team swept aside at home in Thursday's game.
"He asked leave, he had lost motivation and when the leader has no motivation, your only option is to look for another alternative," director Toninho Moreira told reporters.
Midfielder Willie put Vasco ahead early in the second half and two goals from forward Marlone completed another miserable evening for Nautico, who have lost their last 12 games and have only eight points from 17 matches.
Sao Paulo were already 2-0 down to Criciuma when goalkeeper Rogerio, who has scored more than 100 goals from free kicks and penalties during a remarkable career, saw his effort saved by opposite number Galatto midway through the second half.
"It was my mistake, my incompetence," Rogerio told reporters.
Shortly afterwards, forward Aloisio pulled one back for Sao Paulo but it was not enough and the defeat left the six-times Brazilian champions languishing in the relegation zone in 18th place.
Criciuma had taken control with first-half goals from Marcel, from a penalty, and Lins.
Rogerio had previously missed penalties against Portuguesa in the Brazilian championship and in a friendly against Bayern Munich.
The 40-year-old, due to retire at the end of the year, is in his 21st season at the club where he has won every possible title including the Brazilian championship, the Paulista championship, the Club World Cup and Libertadores Cup.
However, he now runs the risk of ending his career with relegation to Serie B.
Hyuri scored one of the best goals of the season as Botafogo climbed to third, four points behind leaders Cruzeiro.
Collecting the ball near the touchline, the 21-year-old swept past one defender, cut inside another, then beat another two with by dragging the ball back and turning before clipped his shot into the net, putting Botafogo 3-0 ahead.
He had already opened his account by heading in just before halftime after Rafael Marques had given the hosts an early lead.
Former Fenerbahce playmaker Alex pulled one back from a penalty.
- Sports & Recreation
- Brazilian championship