Daniel Evans of Great Britain celebrates a point in his first round match against Tatsuma Ito of Japan during day one of the 2019 Australian Open at Melbourne Park on January 14, 2019 in Melbourne, Australia.
It was a hard-fought battle with Evans struggling to attack with any conviction but finally clinching victory in a third-set tight tie-break on his third match point.
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He will now face 20-time Grand Slam champion Federer, if the Swiss overcomes Denis Istomin in his first-round match later on Monday.
Elsewhere, Kevin Anderson survived a brief scare in his first-round match against France's Adrian Mannarino.
The South African No 5 seed, who reached the final of Wimbledon last year, dropped the second set but recovered to win convincingly in the end, with a 6-3 5-7 6-2 6-1 victory.
Girgor Dimitrov also progressed despite getting off to a sluggish start, when he dropped a set against Serbia's Janko Tipsarevic, before recovering to win 4-6 6-3 6-1 6-4.
And there were good results for two top 20-year-olds on tour, with Stefanos Tsitsipas beating Matteo Berrettini 6-7 6-4 6-3 7-6 and Frances Tiafoe strolling past India's Prajnesh Gunneswaran 7-6 6-3 6-3.