The fifth-seeded Cilic, the Zagreb champion in 2009, 2010 and 2013, halted Phau's impressive run from qualifying.
Cilic opened the semifinal a bit shaky and had problems holding serve in the first four games, saving two break points. Phau saved five match points before Cilic served for the match.
Cilic will face German Tommy Haas in the final. The top-seeded Haas defeated British lucky loser Daniel Evans, 5-7, 6-4, 6-3.
It will be the eighth time in the tournament's nine-year history that a singles final features a Croatian.