The 14th seed swept aside the 17-time major winner in well under the two-hour mark, winning 6-3 6-4 6-4 to set up a clash with Kei Nishikori - also a debutant in a Slam final.
History seemed to be repeating itself for the Swiss, who suffered a break of serve to find himself 3-1 down after a lacklustre start at Flushing Meadows.
Federer failed in his bid to break back as Cilic refused to surrender his serve on his way to winning the first set by a three-game margin.
Another broken serve in the first game of the second set proved decisive, however, as Cilic maintained his own solid service game to move two sets ahead and bid to succeed where Monfils failed.
A jittery Cilic was broken for the first time in the match as Federer took a two-game lead in the third set, but the Croat broke straight back before levelling up at two apiece.
However, Cilic, whose previous best in a Grand Slam was a semi-final place at the 2010 Australian open, inflicted his most important break of the match to move 4-3 ahead, before holding serve to reach his first major final.