The top seed Caroline Wozniacki has won her first round match at the ASB Classic tennis tournament in Auckland, beating Germany's Laura Siegemund 6-3 6-2.
The Danish world number three will meet Canada's Bianca Andreescu in the second round.
Third seed Su-wei Hsieh of Taiwan has beaten Monica Puig 6-1 7-6.
Earlier, the seventh seed Kirsten Flipkens was knocked out in her second round match by Spain's Sara Sorribes Tormo.
The Belgian lost the first set but came back in the second, however Sorribes Tormo regathered to win the third, earning a place in the quarter-finals.
Meanwhile, New Zealand tennis player Paige Hourigan and Taylor Townsend from the USA, have won their doubles match to advance to the semi-finals.