The second seeded Indo-American pair overcame a stiff resistance from the American-Canadian pair for 6-3 6-7(2) 10-7 win in the quarter-finals of the euro 528,135 hard court event.
Bopanna and Fleming next face third seeded pair of Austria's Julian Knowle and Slovakia's Filip Polasek, who had an easy 6-4 6-2 win over Jerzy Janowicz and Frederik Nielsen.
India's singles challenge had ended with the defeat of Somdev Devvarman, who went down fighting against Australia's Bernad Tomic in the second round.