“So I knew ‘Serena, you’ve got to come out hot, you’ve got to come out firing’,” said Serena Williams about her clash with Eugenie Bouchard. Photo: Aaron Favila/AP

MELBOURNE – Serena Williams stormed past Canada’s Eugenie Bouchard and into the Australian Open third round on Thursday as her quest for a record-equalling 24th Grand Slam title gathered pace.

The American won 6-2 6-2 in 70 minutes, setting up unseeded Ukrainian teenager Dayana Yastremska as the next hurdle in her bid for another major to equal the mark set by Australian great Margaret Court.

The 37-year-old won her 23rd major Down Under two years ago while two months pregnant, and is the bookies’ favourite to claim an eighth Australian title, despite being seeded 16th.

Williams said she was wary of Bouchard, who is on the comeback trail after a slide down the rankings to number 79 in the world.

“It wasn’t an easy match tonight. Eugenie’s been to the final of Wimbledon (in 2014) and the semi-finals of other Grand Slams,” she said.

“So I knew ‘Serena, you’ve got to come out hot, you’ve got to come out firing’. She’s a really good player, and I haven’t had many matches since last year.”

The signs looked ominous for Bouchard when she won only one point on her opening service game, and then failed to hit a return when it was Williams’ turn to serve. 

Yet the first set was a messy affair for both players, with only two games going on serve.

It was testament to Bouchard’s tenacity that she managed two breaks to four against Williams’ howitzer serve, sending her supporters into raptures. 

But it always looked like an exercise in damage control for the Canadian, who attempted to run Williams around the court, but struggled to cope with her opponent’s blistering power.

Her resistance was slightly more effective early in the second set, when she managed to hold her two service games. 

Williams responded with a lift in intensity, going on a five-game winning streak to settle the match.