Argentina were finalists in 2006, 2008 and 2011, but have never won the event.
Argentina will then roll out their own big gun, Juan Martin del Potro, against the home team's Ivo Karlovic.
Cilic is the only top 10 player featuring at the final, but Del Potro is many fans' comeback player of the season with his run to the Olympics final.
Argentina were finalists in 2006, 2008 and 2011, but have never won the event. Croatia last won the Cup in 2005.
Schedule (starts 1300 GMT)
Marin Cilic (CRO) v Federic Delbonis (ARG)
Ivo Karlovic (CRO) v Juan Martin del Potro (ARG)