Santos were struggling until 10 days ago but have won three games in a row since Neymar returned from playing in the Olympic Games soccer tournament.
Palmeiras took the lead in the 40th minute of Saturday's game when Correa scored with a low shot from the edge of the area, but Santos replied before the break when Neymar curled a majestic free kick into the top-left corner from 30 metres.
Just after the hour, the 20-year-old Neymar, who is reported to be on the radar of some of Europe's biggest clubs, scored again with a weakly-struck low shot from 25 metres which crept in off the foot of the post.
It was not such a happy match for Santos midfielder Paulo Henrique Ganso, who was jeered by his team's supporters following reports he wanted to leave the club.
Santos climbed to ninth with 26 points from 19 games as they completed the first half of their campaign while Palmeiras, under former Brazil and Portugal coach Scolari, have dropped to 16th in the 20-team table.
Midfielder Thiago Neves scored both goals to give Fluminense, second with 42 points, a 2-1 win over third-placed Vasco da Gama in a Rio de Janeiro derby, Vasco replying with an own goal by Gum.
Vasco were furious with the refereeing, complaining that Fluminense's first goal should have been disallowed and that they should have been awarded a penalty.