British number three Naomi Broady beat a top-20 ranked opponent for the first time as she knocked out former world number one Ana Ivanovic in the first round of the ASB Classic in Auckland.
Broady is ranked 122 in the world but beat world number 16 Ivanovic 7-5 6-4.
The 2015 champion Venus Williams lost to Russian Darya Kasatkina 6-7 (7-4) 6-3 6-3.
British number one Johanna Konta was beaten by qualifier Qiang Wang in the first round of the Shenzhen Open.
Konta, ranked 48 in the world, lost 6-3 3-6 6-3 to the 110-ranked Chinese in a match that lasted just under two hours.
It was a disappointing start to the year for the Sydney-born player, who climbed more than 100 places in the rankings in 2015 and reached the last 16 of the US Open.
Both tournaments are regarded as warm-up events for the Australian Open, which starts on 18 January.