Giliati was originally selected in the second round of the 2004 QMJHL Draft by the Shawinigan Cataractes, and made the team in his first attempt. In 2004-05, Giliati's first in the QMJHL, Giliati initially received limited playing time on the fourth line of the team. However, Giliati impressed team management enough to have his role on the team increased. Such added playing time allowed Giliati to finish with 14 points in 54 games. Giliati was then traded to the Lewiston MAINEiacs in the 2005-06 off-season in the trade that sent Atlanta prospect Alex Bourret to Shawinigan. Giliati was an intended offensive replacement for Bourret. Giliati was unable to be a dominant offensive force for Lewiston, bit was able to record 49 points in 70 games. Giliati was praised for his durability and up-tempo style of play. Giliati's offensive abilities continued to grow over the next few seasons with the MAINEiacs. Giliati recorded 24 goals and 57 points in 68 games in the 2007-07 season. Giliati's best season in the QMJHL came in his last season with Lewiston, as he put up a career-high of 40 goals and 87 points in 65 games with the team.
At the conclusion of Giliati's minor career, he went undrafted in the NHL draft, but was signed to an entry-level contract with the Toronto Marlies, the AHL affiliate of the Toronto Maple Leafs. Giliati made his professional hockey debut with the Marlies during the 2007-08 season, playing in one regular season game with the team.