The third seeded Indo-Pak pair dominated the proceedings from the very beginning and eventually posted an easy 6-1, 6-2 win over Rosol and Sousa.
They took just 44 minutes to wrap up the match.
Bopanna and Qureshi will take on Daniel Nestor and Nenad Zimonjic in the final on Saturday.
The Indo-Pak duo won 69 per cent of first serve points, while 50 per cent of points when the opponent got their first ball in.
While Rosol and Sousa could manage to save as many as four break points out of six that their opponents got in the opening set, they simply failed to save any of the two that they received in the second set.
Bopanna and Qureshi continued to press their opponents, dictating play at the net with short sharp volleys.
Image: Rohan Bopanna and Aisam-Ul-Haq Qureshi
Photograph: Brendon Thorne/Getty Images
Sydney International: Bopanna-Qureshi advance, Paes-Stepanek out
Bopanna-Qureshi score first win of season in Sydney
Davis Cup: 'Serbia left Ferrari in the garage'
Sydney: Pironkova wins first title; Del Potro, Tomic to meet in final
Apia International: Somdev advances to second round in Sydney