The hard-hitting Italian, a former world No. 30 who reached the fourth round in New York five years ago, traded blow for blow with the powerful American, but she was broken in the first set, which she lost 6-4.

Giorgi, who was beaten at the quarter-final stage at Wimbledon by Williams' sister, Serena, maintained her high standards in the second set before she lost her serve again, going down 7-5.

Two-time champion Venus will meet Serena in the third round on Friday.