Evans beat defending champion Frances Tiafoe in the opening round of the ATP 250 event in Florida, and continued his run on Friday with a straight-sets win over 35-year-old Seppi.
A fast start saw Evans break twice to lead 4-0, and held off a mini-fightback to take the opening set.
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Evans then saved break point in a mammoth second game of the second set, breaking in the next game before closing out the match.
Awaiting the 28-year-old in the last four will be the winner of John Isner’s match with Adrian Mannarino.
Top seed Juan Martin del Potro is still in the draw and could yet face Evans in Sunday's final.
Evans is expected to rise into the top 120 after his recent form and is closing in on the top 100.
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