Croatian tennis veteran Mirjana Lucic-Baroni is now an Australian Open quarter-finalist and has celebrated with an expletive-laden court-side victory speech.

The 34-year-old beat American qualifier Jennifer Brady 6-4 6-2 to book her place in the final eight at Melbourne.

The last time she made the quarters at a Grand Slam was all the way back in 1999 at Wimbledon, but she never looked like missing out on the opportunity to repeat the dose today, when she bossed Brady off the court.

Lucic-Baroni hit 35 winners to 11 and sent down four aces.

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But her best moment came after the match in her on-court interview, when she won the crowd over with some practical advice.

"I'm a tough little cookie and really, really stubborn," said Lucic-Baroni. "When I want something I will work really hard and do whatever it takes to get there.

"I would tell anybody struggling out there ... actually no, the TV is here and I'm going to get fined."

She was given the all-clear to say whatever she wanted and the crowd loved it.

"F*** everything and f*** everybody, whoever tells you you can't do it, just show up and do it with your heart."