The pair of straight-set victories in Perth put the tie out of reach and sent the Poles into a clash against either Norway or France in Sydney.
Adrian Mannarino and Caroline Garcia had earlier pushed France into a last eight tie against the Norwegians with victory over Italy.
Hurkacz secured a clinical 6-3, 6-4 defeat of Zhang Zhizhen before world number one Swiatek followed up, winning nine games on the trot at one point to beat Zheng Qinwen 6-2, 6-3 despite losing serve twice.
Swiatek was eager to get to Sydney as the first nation to qualify for the semi-finals of the 18-nation mixed team tournament.
"Bondi Beach here we come," she said, after swatting aside Zheng who was the 2023 WTA Most Improved Player. "I'm looking forward to a day off.
"I'm really happy with my game, and also how the atmosphere in the team is," added Swiatek.
"I really feel like we can just be better when we’re together, so for sure playing (with Hurkacz) is an exciting thing to do, and I'm real happy with every match that I play here."
Hurkacz fired 10 aces as he dismissed Chinese number one Zhang.
"It's always a tough match with him. He can play some amazing shots," the winner said.
'Went my way'
In Sydney, journeyman Mannarino, who enjoyed his best-ever season last year, swept past Lorenzo Sonego 6-4, 6-4 before Garcia overcame a stubborn Jasmine Paolini 6-4, 5-7, 6-4.
It gave France an unassailable 2-0 lead to put them into the knockout rounds.
The last quarter-final slot was secured by Greece, with Stefanos Tsitsipas beating Canada's Steven Diez in straight sets and Maria Sakkari overcoming Leylah Fernandez 7-6, 6-3.
The Sydney quarter-finals are played on Thursday and Friday before the semis on Saturday and the final a day later.
The 35-year-old Mannarino won titles at Astana, Newport and Sofia last season to clock a personal best 43 wins, propelling him to a career-high 22.
After opening his season with a loss to world number seven Alexander Zverev, the no-frills Frenchman proved too hot for 46th-ranked Sonego on a scorching day at Ken Rosewall Arena.
"It's always a tough match with him and in the second set I felt it could go either way," Mannarino said. "I was lucky at four-all to go the break up and everything went my way today."
The Frenchman did not face a break point and was solid throughout, especially on second serve, winning 13 of 18 points.
Garcia, who has slipped to 20 in the rankings after hitting a career-high four in 2018, finished the job against Paolini.
But the 29th-ranked Italian refused to go quietly, pushing it to three hard sets over 2hr 16min before Garcia served to love and banked the victory.
Djokovic shocked
Novak Djokovic crashed to his first defeat of the season with a stunning 6-4, 6-4 loss to Alex de Minaur who helped Australia to an impressive quarter-final win on Wednesday.
Ajla Tomljanovic beat Natalija Stevanovic in the second match of the tie to seal Australia's spot in the final four.
Djokovic was hampered by a right wrist problem in Serbia's victory over Czech Republic on Tuesday and the world number one had it worked on again by a trainer before De Minaur earned a late break and went on to clinch the opening set.
Australian Open champion Djokovic dropped serve yet again to hand De Minaur a 4-3 advantage in the second set and saved three match points later, but was unable to prevent the shock loss.
"It's extremely special," world number 12 De Minaur said after the biggest win of his career. "Novak's an unbelievable competitor and what he's done for the sport is pretty special.
"It feels surreal, it feels amazing and I'm happy to do it here in Perth and in Australia.
"Ultimately when you go against Novak, you've just got to go out there, try and enjoy, back yourself and no matter what, keep fighting till the end. Today was my day. I'm happy I was able to get the win. This one definitely means a lot."
The Australian Open runs from on January 14th-28th.