Walter, standing in for first-choice Cassio, who was with the Brazil team preparing for the Copa America, put on an excellent display to keep the scoreline blank.
The result leaves Corinthians in eighth spot in Serie A with 12 points from seven games, while Cruzeiro sit six places behind them with eight points from eight matches.
Palmeiras top the league after edging Athletico Paranaense 1-0 earlier on Saturday.
(Reporting by Andrew Downie; Editing by Greg Stutchbury)
