Cilic, 33, won his second championship in St. Petersburg, becoming the first Croatian to do so. He had already received the award in 2011.
It was his fourth victory in Russia, after two victories in Moscow in 2014 and 2015, where he had lost the final the previous week.
In addition to Roger Federer (103 championships), Rafael Nadal (88), Novak Djokovic (85), Andy Murray (46) and Juan Martin del Potro, the Croatian is the sixth current player to earn 20 tour-level titles (22).
After Cilic saved a break chance in the third set with a courageous drop shot, Fritz, who celebrated his 24th birthday by defeating compatriot Tommy Paul on Thursday, was victorious in the final set.
With the match tied at 4-4, Cilic took advantage of Fritz’s double-fault on break point to serve out the victory with a forehand volley.