Serena Williams said she was pleased to come through a tough match to improve her fitness after battling back to defeat Christina McHale at the Auckland Classic on Thursday, while world No 1 Ashleigh Barty suffered a surprise defeat at the Brisbane International. With her focus on winning a record-equalling 24th grand slam at the Australian Open later this month, Williams said she needs all the court time she can get after a long off-season since losing September's US Open final. It took the top seed two hours to put away the 27-year-old McHale 3-6, 6-2, 6-3 and advance to a quarter-final with Germany's Laura Siegemund, who ousted teen prodigy Coco Gauff in the second round. "I really need to play matches like that to get to my goals," Williams said. "Tournament time is super-important, match time is good. After losing that first set I'm just glad to be still in the event." McHale used her speed around the court in extended rallies which often produced unforced errors from the 38-year-old Williams in the early stages. But just as it looked as if Williams was in a slump at 1-4 down after five games, the world No 10 got to grips with the blustery conditions and McHale's agility and began to take control. It was the reverse from Gauff, seen as one of the rising stars of tennis, who started strongly against Siegemund but faded as the match wore on. The 31-year-old Siegemund, who played her first WTA qualifier in 2003 before Gauff was born, was up 5-4 and serving when the American teen broke twice to take the first set. But from there, she used her considerable experience to ruffle the 15-year-old, forcing her behind the baseline and then drawing her forward with deft drop shots. "In the first set I had my chances but let it go. So I just tried to keep my level and she started to miss a little bit more, and I guess I just got better and better," Siegemund said. As Gauff showed signs of being rattled, she lost the steeliness she showed when she burst into the limelight last year with a win over Venus Williams on her way to Wimbledon's fourth round as a qualifier. Against Siegemund, she finished with seven double faults and 49 unforced errors, which she put down to youth and inexperience. "I'm still learning and that's the problem that I have," Gauff said. "I didn't play the right way and if I lost playing the right way it would have been fine, but I don't think I was playing the right way." Over in Brisbane, American qualifier Jennifer Brady claimed the first top 10 win of her career with an upset 6-4, 7-6 victory over Barty to advance to the quarter-finals. With the tournament moving into the Pat Rafter Arena at the Queensland Tennis Centre following the end of the ATP Cup group stage, Brady had to contend with not only the Australian top seed, who was given a bye to the last-16, but also a vociferous home crowd. Barty, who had never dropped a set to Brady in two encounters last year, was unable to muster a single break point while the American needed only one break of serve in the opening set before sealing the result in the second set tiebreak. "I'm very happy to get the win," Brady said in a post-match interview. "Ash is obviously a great player and a great person. "It's a little bit surreal. I'm super stoked and I'm shaking a little bit, but I really played well today." Barty, who exited the tournament in the first round in 2018, struck more winners than Brady but the 16 unforced errors opened the door for her American opponent who wrapped up the match in 91 minutes. Brady, who <a href="https://www.thenational.ae/sport/tennis/naomi-osaka-grinds-through-at-brisbane-international-as-maria-sharapova-loses-in-first-round-1.961233">beat Maria Sharapova in the first round</a> after coming through three qualifiers, became the fourth American to qualify for the quarter-finals after Madison Keys, Alison Riske and Danielle Collins