Qualifier and current world No.95 Vukic recorded a 6-4 3-6 6-3 win over Bosnia-Herzegovina's Damir Dzumhur in Tokyo on Thursday afternoon.
The Sydneysider fired down 12 aces to two during his one hour 52-minute triumph.
Vukic won 85 per cent of first-serve points and broke twice from his only two opportunities.
The 29-year-old will next face Germany's Daniel Altmaier, a straight sets winner over seventh-seeded Canadian Denis Shapovalov.
Thompson, who along with Vukic played in the Davis Cup defeat to Belgium in Sydney earlier this month, went down in an opening-round epic that lasted three hours seven minutes.
After splitting the opening two sets, both tiebreakers, with Brandon Nakashima, the 24-year-old Californian came from behind to win 6-7 (6-8) 7-6 (7-4) 6-2.
World No.78 Thompson led the double fault count 5-1 and served 10 aces to match his opponent.
But the 31-year-old from Sydney ran out of steam, leaving Nakashima to set up a last-16 clash with Hungarian qualifier Marton Fucsovics, who upset eighth seed Frances Tiafoe on Wednesday.
World No.1 Carlos Alcaraz suffered an injury scare during his opening match.
The US Open champion looked like he might have to retire after hurting his left ankle in the first set against Argentina's Sebastian Baez but he did not appear unduly troubled thereafter as he eased to a 6-4 6-2 victory.
Alcaraz hobbled then collapsed to the court after pushing off behind the baseline during the first point of the fifth game, and it was clear the Spaniard was concerned about what had happened.
He was treated on court by the physio before walking gingerly back to his chair, where he had the ankle strapped up.
The drama continued with a stoppage for rain and Alcaraz's team did not appear to want him to continue, but the 22-year-old dominated the rest of the match under the roof.
"I was scared too, I'm not going to lie," said Alcaraz.
"I'm just happy that I was able to play after that and play such good tennis ... I will try to recover, to do whatever it takes to be ready for the next round."
With PA.