Neymar, who was suspended for the domestic match had played for a Santos reserve team in their friendly against Major League Soccer's NY Red Bulls in New Jersey on Saturday, while Robinho watched from the stands with a minor thigh problem.
Ituano, whose president and captain is former Middlesbrough, Atletico Madrid and Brazil midfielder Juninho, stung Santos by taking the lead through Joao Leonardo after two minutes.
Santos equalised through Andre 12 minutes later and after Ituano's Carlos Eduardo was sent off for a second yellow card offence, a tackle from behind on Paulo Henrique, in the 26th minute the floodgates opened.
In the final minutes, Ituano also had Luiz Eduardo and goalkeeper Saulo sent off. Saulo was shown a straight red card from bringing down Maikon Leite with Andre converting the penalty to complete the rout and notch a hat-trick.
"Even with two leading absentees, the team were extremely efficient, coming from behind in the score and playing a strong game," coach Dorival Junior said.
Santos lead the Paulista (Sao Paulo) state championship with 35 points from 15 matches.
In the Carioca (Rio de Janeiro) championship, Adriano salvaged a 2-2 draw for Brazilian champions Flamengo in the derby against Botafogo with both his team's goals, the second an injury-time header for the equaliser.
Brazil striker Adriano refused to talk to reporters after the match in protest at media reports of problems in his private life after he was dropped by Flamengo for missing a practice earlier this month.
Botafogo, who secured a place in the Carioca final by winning the first phase of the championship, scored both their goals through Argentine forward German Herrera, his first a penalty.
In the southern Gaucho championship, Gremio ran up an 11th consecutive victory beating Ypiranga 3-1 with two goals from striker Jonas.
Gremio's arch-rivals Internacional were held 2-2 by Pelotas to go four games without winning, including two Libertadores Cup matches.
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