Isner, seeded No. 1 and seeking his second title of the year, fought off Christian Harrison 7-6 (11-9), 4-6, 7-5 and Anderson rallied past Matthew Ebden 6-7 (7-9), 6-2, 6-2.
Isner's quarterfinal opponent will be James Blake in what will be only the third meeting between the Americans. Isner has won both previous confrontations, one of them coming in this tournament two years ago.
Blake made it to the quarterfinals by downing Evgeny Donskoy 6-3, 6-2.
Denis Istomin was a 7-5, 6-2 winner over Yen-Hsun Lu, creating a quarterfinal matchup with Anderson.
Giraldo and Harrison will meet Friday and the other quarterfinal match will send Lleyton Hewitt against third-seeded Ivan Dodig.