Klaasen and Venus, the third seeds, beat Australian wildcards Jordan Thompson and Lleyton Hewitt 6-3, 7-6 (7/3), 6-2 on Friday.
Last year’s finalists will now await the winners of the match between Dutch-Denmark duo Robin Haase and Frederik Nielsen and British-Australian pair Ken Skupski and John Patrick-Smith.
In the men’s singles, South Africa’s Kevin Anderson , the fourth seed, takes on Argentina’s Guido Pella in the third round on Friday.
The other South African at the event, Lloyd Harris , lost in singles and doubles in the first round.
Sport24
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