Kanepi, ranked 44th in the world, did not go down without a fight, however. After Serena Williams dominated the first set, finishing it off 6-0 in just 15 minutes, Ms. Kanepi staged something of a comeback in the second set, picking up points from some memorable shots including her signature cross-court forehand stroke, as well as rocketing a passing shot on the forehand, and pulling off a couple of great smashes against the American.

The second set finished 6-4 to Ms. Kanepi, but Ms. Williams got the better of her in the third set, staying ahead throughout and winning 6-3 on the first of three matchpoints in front of a home crowd. The whole match lasted one hour 37 minutes.

The game was the fifth time the pair had met, with the Estonian yet to beat the former world number one. However the 34 year-old Kanepi, from Haapsalu, can draw some comfort from the scoreline: in the second round Serena Williams cruised past her own sister, Venus, in straight sets, 6-1, 6-2. Ms. Kanepi also pulled off a memorable victory against the current world number one, Simona Halep of Romania, in the first round of the competition.

This time last year, Kanepi went one round further, reaching the quarter finals at the USTA Billie Jean King National Tennis Center, losing that time to another American, Madison Keys.

The game came one day after the first birthday of Serena Williams' first child; Ms. Williams had also attracted attention through the summer after donning a catsuit-type outfit at the French Open in May, a sartorial move which was subsequently banned by French tennis authorities.

Top Estonian ladies' player Anett Kontaveit (27th in the world) was knocked out in round one of the tournament.

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