The Italian was defeated 6-4 6-2 by world number 20 Draper, who achieved his first win since losing to Jannik Sinner in the US Open semifinals earlier this month.
With the win, the 22-year-old resumes his form following a dismal Davis Cup in Manchester, where he lost both of his singles matches.
Felix Auger-Aliassime of Canada and Francisco Cerundolo of Argentina defeated Draper in straight sets, preventing Great Britain from progressing to the next round.
In Tokyo, Draper overcame world number 103 Belluci in the first set by edging it, then cruising to victory in the second set as he took a 5-1 lead.
On Friday, Draper will take on Hubert Hurkacz, the second seed from Poland.
Meanwhile, American Alex Michelsen defeated Greek fourth seed Stefanos Tsitsipas 4-6 6-1 6-2.
The sixth seed from America In a match that lasted three hours and twelve minutes, Yoshihito Nishioka of Japan defeated Auger-Aliassime 7-6 (7-5) 3-6 7-6 (7-5) while Tommy Paul defeated Matteo Arnaldi of Italy 6-3 6-2.
