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, HC 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.[2] Giliati scored his first goal for Blues on September 20, 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.[3] He left Zagreb after one year and headed to Switzerland,[4] where he played in three games for HC Davos of the National League A (NLA) at the beginning of the 2016-17 campaign. In October 2016, he transferred to the Schwenninger Wild Wings of the German top-flight Deutsche Eishockey Liga (DEL).[5]
In his third season with the Wild Wings in 2018–19 and with the club well out of playoff contention, Giliati left in the final season of his contract to sign for the remainder of the year with Swiss outfit, the SCL Tigers of the NL, on February 7, 2019.[6]
After 11 European seasons, Giliati opted to return to North America in agreeing to a one-year contract with the Fort Wayne Komets of the ECHL for the 2022–23 season on July 21, 2022.[7]