Isner is currently ranked 15th in the world after having reached a career best No. 9 last April.
He defeated Anderson 6-2, 7-6 (7-1) to create a semifinal matchup with Edouard Roger-Vasselin, who was a 6-4, 6-3 winner over Ricardas Berankis.
Isner's other semifinal appearance this year was in San Jose, Calif., and resulted in a loss to Tommy Haas.
Haas is also alive in this tournament, having moved into the semifinals by defeating Ivan Dodig 7-6 (8-6), 2-6, 6-1.
Ernests Gulbis will meet Haas in the semifinals after downing Daniel Munoz-De La Nava 6-1, 6-4.
Isner has won five titles in his career, two of them coming last year.
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