Ana Ivanovic kept her Australian Open preparations on track with a narrow win over Italy's Roberta Vinci in Brisbane.
The world number five saved two match points to win 6-7 (4-7) 7-5 6-1, and will next face Amelie Mauresmo.
Former world number one Mauresmo battled to a 5-7 6-2 7-6 (13-11) win over fellow Frenchwoman Julie Coin.
In the men's event, Ernests Gulbis could not back up his opening win over top seed Novak Djokovic as he lost 6-3 6-4 to Paul-Henri Mathieu.
Second seed Jo-Wilfried Tsonga suffered a scare before beating Jarkko Nieminen 0-6 7-6 (7-1) 7-6 (7-5).
"I wasn't as aggressive as I should have been"
Third seed Fernando Verdasco of Spain beat Croatia's Mario Ancic 6-2 6-3.
Ivanovic, 21, faced two set points at 15-40 in the 10th game of the second set but came through to take three straight games, followed by nine of the first 10 points in the decider as she raced 5-0 ahead.
"It was really tough," said the Serb. "She was playing really well, mixing it up a lot. I wasn't as aggressive as I should have been.
"I tried to be fitter and tougher mentally than she was and it paid off, so that gives me confidence."
Mauresmo, 29, recovered from 2-5 down in the third set to defeat Coin after three hours 14 minutes - her longest ever tour match.
"It was a strange one," said Mauresmo. "I really don't know what to say about this match.
"I'm just glad I won it because it would have really been the 'missed-occasions match' if I didn't. That's the good and positive point for today."
In the Hopman Cup in Perth, Germany won a tie-break in the deciding mixed doubles to knock out the United States.
Nicolas Kiefer and Sabine Lisicki teamed up to defeat James Blake and Meghann Shaughnessy 6-3 3-6 10-7.
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