The 20-year-old took his tally to 12 goals in the competition even though he has missed a number of games due to international commitments including a three-week spell at the Olympic Games.
Neymar opened his account in the 11th minute of Saturday night's game by nonchalantly diverting a low cross into the net at the near post and slotted in another from near the penalty spot after sloppy Cruzeiro defending in the 35th.
He then turned provider, setting up the third for Felipe Anderson with a run down the right and low cross in the 52nd minute, and completed his hat-trick in by converting an easy chance set up by Ezequiel Miralles.
Santos are ninth in the table with 46 points from 33 games, three ahead of Cruzeiro.
"I'm overcome, it makes me want to cry," Neymar told reporters after Cruzeiro fans, who had initially booed their own team, chanted his name and applauded him off the pitch.
Ten-man Gremio scored in the last minute to beat Ponte Preta 1-0 and stay third with 63 points, nine behind leaders Fluminense.
Gremio had Julio Cesar sent off midway through the second half but Vanderlei Luxemburgo's team took the points when Andre Lima headed in from corner.