Ajla Tomljanovic is taking her new-found responsibility in her stride as she eyes another deep run at Wimbledon.

Tomljanovic surged into the third round with a 6-2 6-2 dispatch of American qualifier Catherine Harrison, showing no signs of caving in to the pressure of filling the impossible shoes of retired reigning champion Ash Barty.

The 29-year-old had too much firepower for Harrison, seeing off the Wimbledon debutant in one hour, 26 minutes on Thursday.

A quarter-final loser to Ash Barty last year, Tomljanovic is doing an admirable job stepping up as Australian tennis's new women's No.1 following the shock retirement of her top-ranked compatriot in March.

The world No.45 is yet to drop a set this campaign, conceding only nine games en route to the last 32.

But Tomljanovic is not being weighed down by the heavy burden of having to follow Barty and carry Australia's women's title hopes at the All England Club.

"Not having Ash here - she is such a big presence in the Aussie tennis world - it does feel like there's a little bit more responsibility, but at the same time I'm just focusing on myself," she said.

"Today was really good. I wasn't feeling too sharp when I woke up, a bit lethargic. Maybe that made me feel a little bit more alert when I started.

"I didn't really know what to expect from her (Harrison), but I knew she had four great wins to get to this stage.

"I played her actually in doubles at the French and noticed that her serve was pretty good, especially from her height. I knew it would be a tricky match but, yeah, I felt really good off the ground."

Tomljanovic next plays 2021 French Open champion Barbora Krejcikova, the 13th seed after an injury-ravaged year, on Saturday and could meet world No.1 Iga Swiatek in the round of 16.

Tomljanovic assumed control against Harrison after grabbing the first break of the match in a marathon 12-minute third game that featured 10 deuces.

She finally won the game on her fifth break point when Harrison, under relentless pressure, coughed up a double fault.

Shooting for the lines, Tomljanovic reeled off five games in a row and took the opening set after forcing the American into another error through the sheer weight of her booming groundstrokes.

After dropping serve for the only time early in the second set, Tomljanovic wrestled back control immediately, winning the next four games to advance in confident fashion.

"It feels good to be in the third round again," she said.

"Just the familiarity of Wimbledon and playing on the grass without thinking about it, it's kind of in my mind a little bit, so it definitely helps."