The Briton's win against the eighth-seeded American earned him the chance to atone for his loss to Karen Khachanov last week in Adelaide — the third-seeded Khachanov defeated Marc-Andrea Huesler 6-4, 6-4 later in the day to set a quarter-final clash with the 21-year-old Draper.
Well established as a strong server with his 6-foot-4 frame, Draper has excelled on return this week. After breaking four times in his opening victory against Lorenzo Sonego, he converted on three of five break chances against Paul, who was playing in his first event of the new season.
Broken just once, Draper fired 10 aces and won 88 per cent of his first-serve points in the win.
Also in early Wednesday action, seventh seed Alejandro Davidovich Fokina advanced with a 6-3, 6-3 win against home favourite John Millman.
He will next face fellow Spaniard and second seed Roberto Bautista Agut, who downed Dutch lucky loser Robin Haase 6-3, 3-6, 6-3.