Alcaraz advanced with a commanding 6-2 6-4 win over American Brandon Nakashima on Sunday, to set up a clash with Norway's Casper Ruud.
The fourth-seeded Ruud blazed past Vukic with a clinical 6-3 6-2 win.
Despite Sunday's loss, it was a great tournament for the Australian, who fought his way through qualifying, then posted victories over experienced players Damir Dzumhur and Daniel Altmaier to reach the quarter-finals.
In other action on Sunday, Danish third seed Holger Rune was sent packing by American Jenson Brooksby.
Alcaraz, who overcame an injury scare in his straight-sets win over Argentine Sebastian Baez in Thursday's opener, showed scintillating form to dispatch Nakashima for his 65th win of the season, thumping 39 winners in the one-hour 20-minute contest.
The 22-year-old Spaniard, fresh from reclaiming top spot in the world rankings after clinching his sixth grand slam title at the US Open this month, showed he is in fine form ahead of his clash with Ruud.
"These kind of matches help to keep my confidence really, really high. I played some great tennis," Alcaraz said.
"It's great to go through, to play another semi-final. It's special, because it's the first time I'm playing in Japan, here in Tokyo. To reach the semis in my first appearance is something great."
The biggest upset of the day came in Rune's 6-3 6-3 loss to American Brooksby, ranked No.86 in the world.
"Once I get on a roll from a couple of matches, I just think I'm really able to get into my zone. I think that's one of my big strengths," Brooksby said.
"I thought I had a pretty good plan on him coming out here. I had never played him before, but I think that's good maybe, someone who hasn't faced my unique skills, I guess.
"I had a good rhythm from the first two matches and thought I was playing really good tennis, and I think I just stayed a little bit more consistent today."
Wimbledon semi-finalist Taylor Fritz overcame a second-set blip to beat Sebastian Korda 6-3 6-7 (5-7) 6-3 in an all-American clash.
Second seed Fritz, set to climb to fourth in the ATP rankings on Monday, overtaking Novak Djokovic, will take on Brooksby in the semis.
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