The top-seeded Swede has won 17 of 18 matches this year, clinching titles in Rotterdam last weekend and in Brisbane last month.
Soderling slammed an ace clocked at 134 mph to set up three match points, and the Swede converted the first with a forehand winner down the line.
The French Open finalist saved four set points in the tiebreaker of the first set, but Cilic converted the fifth when a backhand return from Soderling sailed wide.
Soderling hit a forehand pass down the line to take a 4-3 lead in the next set. He leveled at one set apiece when Cilic hit an approach shot wide.