The unseeded Indian pair upset the American-German combo 6-4 3-6 10-8 in the quarter-finals contest, which lasted one hour and 10 minutes.
Divij and Purav were broken in the very first game of the match and were down 0-3 but went on to win six out of the next seven games to pocket the first set.
They broke Rajeev's serve at 1-3 and Benjamin's serve at 4-all.
Becker had got the better of Andre Agassi in his last match of his career at the US Open. His current ranking is 95 in singles with a career best of 38.
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The Garman was ranked as high as 58 in doubles in 2010.
Rajeev, who formed a team with India's Rohan Bopanna early this year before switching partner, is ranked 44 in doubles with a career high ranking of 33 in 2010.
Divij and Purav next play Croats Marin Draganja and Mate Pavic, who had knocked out top seeded Thai pair of Sonchai Ratiwatana and Sonchat Ratiwatana in the 1st round.