Edmund's hopes of making it to a first final were ended in emphatic fashion by his sixth-seed opponent, who came out on top 6-3 7-6(4) 6-2 in a match lasting two hours and 20 minutes.
Cilic, who had also never previously reached the final of this competition, will now face either defending champion Roger Federer or Hyeon Chung on Sunday.
A gruelling fortnight Down Under took its toll on Edmund, as he lost serve twice in the opening set and required a medical timeout.
Both men held in a tight second set, but it was Cilic who took the tie-break with his second set point to pave the way for a convincing win.
Edmund, expected to rise to 25th in the latest men's singles rankings next week, struggled in the final set as his Croatian opponent again held throughout and earned breaks in the third and seventh games.