Williams has already installed herself as the underdog for the next round [AFP]

The calm nature of the match contrasted starkly with the American's ill-tempered encounter in the previous round which ended with her labelling her opponent a "cheat" following a dispute over a point.

The 10-times grand slam champion was barely bothered by 24th seed Wozniak, racing through the opening set in 23 minutes and said she sensed the Canadian was not used playing on the main showcourt.

"After I got off to such a quick start, I realised that maybe she hadn't played on Centre Court yet," she said.

"Maybe she hadn't had the experience in big matches in grand slams where there is a chance for either player who won to get into the quarter-finals."

Wozniak agreed with her assessment.

First time

"It's my first time on Philippe Chatrier," she said. 

"Emotions get involved and you just get tight and you can't play really your game, so it's tough.

"I was like a rock. I couldn't let go on my shots and play my game."

It took Williams just half an hour to clinch the second, wrapping up victory on her second match point when Wozniak netted a service return.

"I feel like it was my most focused match so far," said Williams, who berated herself for a "junior tennis" display in her first round match when she needed three sets and nine match points to stamp out Czech Klara Zakopalova's challenge.

The 2002 champion will next face in-form Russian seventh seed Svetlana Kuznetsova and was quick to install herself as the underdog.

"She's playing unbelievable on clay. I think she's been doing really, really good in this tournament, as well," said Williams – at 27 the oldest woman left in the draw.

"Honestly, I feel like I have nothing to lose. She's an excellent clay court player, so it'll be fun."

Kuznetsova survived her stiffest test yet to beat Pole Agnieszka Radwanska 6-4 1-6 6-1 earlier on Monday.