The Australian qualifier and current world No.95 scored an 84-minute 6-4 6-2 victory on Friday and will next face fourth seed Casper Ruud.
The Norwegian crushed Italy's Matteo Berrettini 7-6 (7-4) 6-2 in one hour 39 minutes in the final match of the night.
Earlier, Vukic broke three times on his way to the next round and the 29-year-old held all of his nine service games.
The Sydneysider did not face a single break point on his ball.
Also through to the last eight is Sebastian Korda, a 6-1 6-4 winner over Sho Shimabukuro of Japan.
Korda will next face fellow American Taylor Fritz, after the 2022 champion got past Nuno Borges 7-5 7-6 (7-4) to reach his 10th quarter-final of the season.
"I think at times I made it very hard for myself," world No.5 Fritz said.
"I came out first game and was broken. The court I warmed up on was super fast to centre court, and I didn't make first serves in the first game and then caught every ball super early.
"It is not too often I go down a break early and then went down a break down two times in the second set, but I fought really hard and did a great job of getting myself back in the sets."
Fritz has earned a Tour-leading 30 wins since the start of the grass swing in June and has so far added another 100 points to his tally this week in Tokyo, boosting his chances of returning to the ATP Finals in November.
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