Cilic reached the fourth round at Roland Garros in 2009 and 2010 but he lasted less than three hours at this year's tournament before going down 7-6 (7-5), 6-4, 6-4.
The 19th seeded Croat has had a poor year by the standards he set in 2009 and early 2010 and never looked comfortable against world no.?100 Ramirez Hidalgo.
Seventh seed David Ferrer took only an hour and 25 minutes to see off Jarkko Nieminen 6-3, 6-3, 6-1, while French favourite Jo-Wilfried Tsonga followed the Spaniard on to Court Philippe Chatrier and defeated Czech Jan Hajek 6-3, 6-2, 6-2.
Stanislas Wawrinka, who could meet Swiss compatriot Roger Federer in the last 16, did not have the ideal first set against French qualifier Augustin Gensse, but fought back to win 4-6, 6-3, 6-4, 6-2. His fortunes were better than Latvia's Ernests Gulbis, who suffered his sixth successive first-round defeat at grand slams, losing 6-1, 6-4, 6-2 to Blaz Kavcic.
On the women's side of the draw, last year's runner-up Sam Stosur defeated Iveta Benesova 6-2, 6-3, while Jelena Jankovic progressed with a 6-3, 6-1 win over Alona Bondarenko. Former champion Svetlana Kuznetsova also made it through with a 6-2, 6-3 win over Maria Rybarikova.
Novak Djokovic and Roger Federer begin their campaigns today against Thiemo de Bakker and Feliciano Lopez respectively, while Andy Murray is due on court tomorrow against French qualifier Eric Prodon.