World number three Caroline Wozniacki cruised into the last 16 at the Auckland Open, beating Madison Brengle for the loss of just three games.

American Brengle stunned Serena Williams in the corresponding tournament 12 months ago, handing the 23-time grand slam winner her only defeat of a truncated 2017, but never looked like replicating that upset as Wozniacki powered through to a meeting with Croatia's Petra Martic.

Brengle kept it tight early on but folded when top seed Wozniacki broke for a 4-2 first-set advantage. The Dane rattled off eight of the next nine games to clinch a 6-3 6-0 victory in just 58 minutes.

"I thought I played pretty well, especially considering it's the first match of the year," Wozniacki said. "It took me a couple of games to just get the rhythm and then I started playing better and better.

"I'm just trying to get my legs moving, trying to make the right decisions, wait for the right shots to play aggressive and go for it, and find the right balance of offence and defence."

There were also wins for third seed Barbora Strycova and fourth seed Agnieszka Radwanska, albeit in more challenging circumstances.

Strycova was pushed all the way by 2012 French Open finalist Sara Errani before coming through 6-4 6-7 (3-7) 6-4 while Radwanska also required three sets before prevailing 6-2 4-6 6-2 against Brazilian Beatriz Haddad Maia.

Three seeds did depart on Tuesday, however, with Lauren Davis, Yulia Putintseva and Mona Barthel all beaten.

Davis was thrashed 6-1 6-2 by fellow American Sachia Vickery, Putintseva went down 6-3 6-3 to Belgium's Ysaline Bonaventure and Barthel succumbed 6-2 6-2 to Varvara Lepchenko.

Elsewhere in the draw there were victories for Viktoria Kuzmova, Taylor Townsend, Johanna Larsson and Veronica Cepede Royg.