Cilic's biggest weapon, his booming serve, lacked its usual accuracy and the German Kohlschreiber was able to control long rallies, pushing the towering Croatian around the court with pinpoint groundstrokes en route to a quick victory.
Cilic, runner-up at this year's Australian Open, only managed to put 51 percent of his first serves in play and was unable to convert any of his four break-point opportunities.
It is the third time that Kohlschreiber has reached the fourth round at the tournament in the California desert and his seventh victory over Cilic in 11 career meetings.
The tournament's number 31 seed will next face Frenchman Pierre-Hugues Herbert, who advanced earlier on Tuesday after his countryman Gael Monfils was forced to retire from their match due to back pain.
(Reporting by Rory Carroll; Editing by Toby Davis)