Isner was stretched to three sets for his third consecutive match, beating American qualifier Rhyne Williams 4-6, 6-3, 6-2.
''Trust me, I'd like to win it in two sets,'' said Isner, the American who is seeded second.
Cilic, the seventh seed, now has won an ATP World Tour-leading 16 matches this season. The Croatian delivered 12 aces in his 6-2, 6-3 win against Gabashvili.
''Good times are rolling,'' Cilic said.
Johnson defeated No. 6 seed Feliciano Lopez 6-3, 6-2. The 24-year-old from the University of Southern California upset top-seeded Tommy Haas two days ago and earned a spot in the semifinals for the first time at an ATP event.
''I'm playing composed tennis and staying within myself,'' said Johnson, who helped USC to four NCAA titles.
Johnson had to win two qualifying matches to earn a spot in the 32-player main draw.
Anderson, ranked No. 21 in the world, got into the semifinals by beating Australian Marinko Matosevic 6-7 (3), 6-3, 6-3.
Neither player broke serve until 3-3 of the second set when Anderson broke Matosevic and went on to close out the set. He also broke Matosevic twice in the first four games of the third set and punctuated the victory with a 131 mph ace on the final point of the match.
''I've played him a couple times before (on the World Tour) and it's a battle each time,'' Anderson said of Matosevic, who has yet to beat the former University of Illinois standout in three ATP matches. ''I just hung in there and finally got that breakthrough in the second set.''