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The 49th-ranked Edmund, the only British man in the main draw after five-times finalist Andy Murray’s injury withdrawal, toughed out a 6-7 (4/7), 6-3, 3-6, 6-3, 6-4 win in almost four hours.
It reversed his loss to the 11th seeded Anderson over five sets in the third round at last year’s French Open.
Edmund’s previous best result at a Slam was his defeat of No.15 Richard Gasquet in the first round at the 2016 US Open.
“Really good result for me. It was great to win at the end like that,” he said.
“So many positive reasons. Just getting through a tough match like that. Also a quality player. Had a good year last year, started the year this year really well.
“My first overall thought — personal satisfaction, the hours you put in, training, so many things like that. Those type of results make it.”
Anderson is one of the biggest servers on the ATP Tour and cranked up a total of 35 aces with a 67 percent first serve, yet Edmund broke him four times.
“Kevin just serves himself out of trouble so much. Very difficult to read it,’ Edmund said.
“So when you get a racquet on the ball, it really has to go in the court. I thought I did a pretty good job.”
It is only the second time he has reached the second round in Melbourne, while South African Anderson, who lost the 2017 Flushing Meadows final to Rafael Nadal, had made the round of 16 in Australia three times.
The victory set Edmund up with an encounter with Uzbek journeyman Denis Istomin.
“You know what you’re going to get with him. He’s going to bring out a level that’s going to be tough to beat because he’s that solid player,” Edmund said.
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