The fourth seeded Indo-Zimbabwean pair went down 6-1 2-6 3-6 to USA's Eric Butorac and Hungarian Timea Babos in a match that lasted for 76 minutes here.
Leander, who missed the French Open due to turbulence in personal life, and Black had won the 2008 US Open, besides clinching titles at Australia and Wimbledon in 2010.
Meanwhile, Indo-Pak men's doubles pair of Rohan Bopanna and Aisam Qureshi were lagging 7-6(3) 6-7(5) 3-6 against Canada's Vasek Pospisil and Jack Sock of USA when play was suspended because of a heavy downpour at the All England Club here.
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