The 20-year-old had to save three match points to eventually triumph 4-6 7-6 (9-7) 6-2 against her Kazakhstani opponent in Melbourne.
Watson will take on Radwanska, who demolished the Briton 6-0 6-2 in the third round of Wimbledon last year, for a place in round four.
But although Watson is expecting a difficult match against the number four seed, she feels she is a “different player” to the one who lost at SW19 back in June.
“She’s a very different player to most of the girls,” said Watson of Radwanska. “She’s consistent, got great feel, so it’s going to be another physical match.
“I’ve played her before, so I’ve got that feeling. I think the first time I played her I just went guns blazing, didn’t know what to do – I just went for way too much.
“This time I’m coming in a different player, and I’m going to approach it differently.”
Watson admits her defeat by Radwanska at Wimbledon was difficult to swallow and vowed to make amends with an improved performance this time around.
“That killed me,” she said. “I was so upset. I was playing at home in front of everyone and I just got wiped off the court. That wasn’t a great experience.
“I feel more experienced and I feel more confident in my game now. This is my second third round now, so I’ve been here before. But I’m just looking forward to playing her again.”
Watson also reserved praise for the support she received during her second-round win over Pervak in Melbourne.
“They were awesome throughout the whole match,” she added. “It’s easy to support someone when they’re winning, but when they’re losing it’s not as easy.
“They were just non-stop from beginning to end supporting me, and it was just unbelievable being out there.”
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BIOGRAPHY: Marcus Rashford