British number four Draper needed only one hour 20 minutes to complete his victory against world number 14 Paul in Adelaide.
Having powered into a 4-0 lead, the 22-year-old broke for a third time at 5-1 to take the opening set.
Paul, who also lost to Draper in Adelaide last year, came out stronger in the second set and managed to hold serve until the Briton got the decisive break at 5-4 and secured the win in style with a superb passing shot down the line.
If Draper beats Bublik in the semi-finals, he would face American Sebastian Korda or Czech seventh seed Jiri Lehecka in the final.
“I’m really impressed with the way I came out today,” said Draper, who survived two match points to beat Miomir Kecmanovic on Wednesday.
“I knew it was going to be difficult, I played a really long match yesterday. I’m really proud of the work I’m doing, showing my physicality on court.
“Each time I play I’m proving myself to be a better player than I thought I was, so a really good match against a great player like Tommy.”
2024-01-11 15:16:00
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