Friday's matches were delayed by rain in humid Chennai.
Cilic, the tournament's second seed, beat Colombia's Santiago Giraldo 7-6 (7-3), 6-1, while Wawrinka, from Lausanne, Switzerland, topped German southpaw Michael Berrer 7-6 (7-5), 6-4.
Cilic also won the Zagreb Indoors tournament in 2009 over fellow Croatian Mario Ancic.
Elsewhere, fourth-seeded Janko Tipsarevic of Serbia beat Dutchman Thiemo De Bakker 7-5, 7-5, and fifth-seeded Dudi Sela of Israel was a 7-6 (7-3), 7-5 winner over Slovakia's Lukas Lacko.
Saturday's semifinal match-ups are Cilic-Tipsarevic and Wawrinka-Sela.
Sunday's winner pockets a $68,450 champion's check.
Copyright 2010 by United Press International.