The 23-year-old, who reached the China Open semi-finals last week, continued his good form with a 6-3 6-4 success over the experienced Italian to set up a tie against world number 48 Nicolas Jarry of Chile in the next round.
Edmund saved a break point in the third game of the match before exchanging three further breaks of serve to come out on top and take the opening set, using his trademark hard-hitting baseline game to good effect.
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Seppi had another break point at the start of the second set but Edmund survived before taking control of the match with a break to go 3-2 ahead.
Edmund maintained his advantage and closed out the match on serve with a forehand winner to reach the last-16 as he chases a first ATP Tour title.
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