AUCKLAND, New Zealand - No.6 seed Venus Williams returned to the quarterfinals of the ASB Classic on Thursday with a straight-set victory over compatriot Lauren Davis, 6-4, 6-3.

The 38-year-old American, the winner in Auckland four years ago in 2015, came out on top in a clash of two former champions, ousting the 2017 champion behind three breaks of serve in just over 90 minutes.

"I think it was even cleaner tennis than the first round, but I'm still searching for perfection. She really can hit the ball," Williams said after the match.

Related: Venus outlasts Azarenka in thrilling Auckland opener

"I'm 6-foot-1 and I'm a foot taller than her, but she hits it just as hard, so I had to be on my toes. She can control the point, so it was kind of a battle of who can do that better, and I was happy to be able to cross the line first."

Neither player faced a break point over the first five games of the match, until Williams struck first by converting her second opportunity in the sixth to move ahead at 4-2. 

Though she failed to convert a set point in the eighth game, and surrendered serve for the only time in the match as she sought to seal the set at the line in the ninth, the American quickly restored order with a second break to finally seal a one-set lead.

"The momentum can change so quickly, so I tried to not let it have a complete momentum change to 5-all," she said. "I think [today] was more consistent [than round one]. It's two completely different players, so it's difficult to measure each one.

"I was really happy to have played well against her. I think I served better throughout the whole match more consistently, so I think that helped me a lot today to close it out."

In set two, the seven-time Grand Slam champion secured the lone break early on, as she converted her fourth break point in the second game, and surrendered just six points on serve overall to book a spot in the last eight.

After defeating a former champion, a former finalist could be on the cards for Williams next, as she will face the winner of the match between top seed and two-time runner-up Caroline Wozniacki and Canadian teenager Bianca Andreescu.

"I haven't played her in a year and a half or so, but she's improved her game so much. She's won a major, the year-end obviously the odds are on her side to win this match and I might see her there," Williams said of the Dane, against whom she owns a 7-1 record.

"I know nothing [about Andreescu]. I have to be able to get out there and do what I do, but it would be nice to see her play a little. The quality of the players is high here, and everyone is trying to find their best form right away.

"It's not east, so there's that pressure of trying to play your best but also trying to play smart. Everyone is trying to get their feet together, and it's hard when you're playing a No.1 player in these early rounds. The doesn't happen too often, and it's an amazing first week.

"The atmosphere is incredible...and it's just great for the players and the fans."