The third-seeded Indo-Russian pair of Paes and Elena Vesnina was stunned by the seventh-seeded Czech duo of Lucie Hradecka and Frantisek Cermak 6-7 (2) 5-7 in a battle that lasted an hour and 43 minutes.
Paes and Elena could win just 67 points as compared to their rivals' 80, while they also committed 25 unforced errors.
Sania along with her British partner Colin Fleming also went down in straight sets to fourth seeds Kveta Peschke of Czech Republic and Poland's Marcin Matkowski.
Unseeded Sania and Fleming failed to match their more fancied opponents in the match to bow out in just 69 minutes, losing 3-6 5-7.
The Indo-British combo wasted as many as seven out of the eight breakpoints they got, to go down tamely.