Rain washed out most of Wednesday's schedule, but the quarterfinals were all set Thursday and will be played Friday.
The top-seeded Isner defeated Go Soeda 7-6 (7-2), 6-2 in the final match of the evening to create a quarterfinal matchup with defending champion Kevin Anderson.
Anderson, the No. 6 seed, survived a battle with Yen-Hsun Lu 6-4, 3-6, 6-3.
Haas was a 6-4, 6-1 winner over Denis Istomin and will next meet Ivan Dodig, who got past Evgeny Donskoy 6-3, 7-5. Haas won this event seven years ago.
The other quarterfinal will send Edouad Roger-Vasselin against Ricardas Berankis. Roger-Vasselin eliminated Ivo Karlovic 6-4, 75 and Berankis rallied to defeat Jack Sock 3-6, 6-4, 6-1.
Sock reached the quarterfinals last week at the U.S. Indoor Championships to climb from 168th in the world to No. 130.