Isner of the United States had to rally to get past Israeli Dudi Sela 3-6, 6-1, 7-6 (7-5) at Delray Beach Tennis Center.
Meanwhile, Cilic -- who titled in Zagreb two weeks ago and finished second in Rotterdam last week -- cruised to a 6-3, 6-4 triumph over American wild card Ryan Harrison.
His quarterfinal opponent will be Russian Teymuraz Gabashvili, who was leading No. 3 Kei Nishikori 4-2 in the first set when the Japanese star retired with a left oblique injury.
Also Thursday, American qualifier Rhyne Williams overcame Cypriot wildcard Marcos Baghdatis 6-7 (7-9), 6-4, 6-2.
Notable deaths of 2014 [PHOTOS]