The top-seeded American, who was watching from the stands, has targeted this week and hopes to follow up her Madrid trophy from the weekend.
The 39th-ranked Robson moved through to the second round in just under 90 minutes against Venus, the 1999 Rome winner now ranked 24th.
Robson, 19, closed it out on her third match point. Venus pulled out of her first match last week with back pain and had reportedly been training at half strength in Rome.
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