The fifth-seeded Cilic beat Tomas Berdych 7-5, 7-6, while Hewitt reached his first semi-final in 11 months by upsetting No 3 seed Juan Martin del Potro 6-2, 2-6, 6-2.
Hewitt took a 4-2 lead with a backhand winner after Del Potro struck consecutive double-faults, and hit a backhand volley to break again for the set. Del Potro sped to a 4-0 lead in winning the second set, but, in the decider, Hewitt broke Del Potro at love to earn a 3-1 lead and broke again at 5-2.
Cilic was under pressure in both sets. He faced a break point at 4-4 but Berdych netted his return, and Cilic failed to convert two set points at 5-4 before Berdych made a forehand error on a third break point at 6-5.
In the second set, Berdych held one break point at 2-2 and another at 4-4, but Cilic once again held on before claiming a tie-break win.