The Serena Williams farewell tour continued in New York on Monday evening as the former world No. 1 booked her spot in the second round of the US Open with a 6-3, 6-3 win over Danka Kovinic.

But it was a rocky start for Williams, hitting five double faults before she steadied to come back from 2-3 down in the first set.

Serena Williams arrives to play Danka Kovinic in her final tournament. Photo: Roger Parker International Sports Fotos Ltd

Then second set went to form, as Williams, 40, improved her service and found her rhythm as a capacity crowd, mostly made up of New York’s liberal elite, plus former US President Bill Clinton, cheered her on.

Next up for the 23-time champion is a second round meeting with World No. 2 Anett Kontaveit on Wednesday.