Career
Giliati played major junior hockey in the Quebec Major Junior Hockey League with the Shawinigan Cataractes and the Lewiston MAINEiacs. Originally signed as a free agent by the Toronto Maple Leafs, on August 27, 2010, Giliati was traded by the Maple Leafs (along with Alex Berry) to the Tampa Bay Lightning in exchange for Matt Lashoff. At the conclusion of his entry-level contract, and released as a free agent by the Lightning, Giliati opted to pursue a career abroad in signing with Italian club, The Human Context Bolzano of the Serie A. Of Italian heritage, Giliati spent a single season with HCB in Italy, helping claim the Italian Championship, before leaving for the Finnish Liiga with SaiPa.
After two seasons with SaiPa, Giliati transferred to fellow Finnish club, Espoo Blues on a one-year contract on April 28, 2014.
Giliati scored his first goal for Blues on September 20th 2014 in a 5-4 away loss to Oulun Kärpät. On July 13, 2015, Giliati left Finland as a free agent to sign a two-year deal with Croatian based KHL entrant, KHL Medveščak Zagreb.