Noskova's win secured a 2-0 win for the Czechs, who will next face either Kazakhstan or Spain as they seek their 12th title in the competition.
"The first match is never easy, no matter what. So, I was surprised by the way that I played in the first set, especially," said the sixth-ranked Noskova, who fired 15 aces and faced no break points.
"Obviously, second set was a lot tougher. Katie served really well and didn't give me many chances, so I had to kind of use anything that I have in the tie-break, and that worked."
Noskova breezed through the opening set and came up with clutch serves at crucial moments in the second to wrap up the match.
Earlier, Czech captain Barbora Strycova selected Marie Bouzkova as her No.2 singles player instead of the eighth-ranked Karolina Muchova - and was rewarded for her choice.
Bouzkova used her all-court prowess and clever net play to put the Czechs in front, surviving a three-hour tug of war with Sonay Kartal to record a 7-6(2), 4-6, 6-4 victory.
World number 127 Kartal was playing her first competitive match in six months after recovering from a spinal stress fracture, and she did well to challenge the 26th-ranked Bouzkova but ultimately faded in the deciding set.
"I think she played incredible. I think not playing for half a year and coming out the way she did, yeah, huge respect for her," said Bouzkova of her 24-year-old opponent.
Quarter-final action resumes on Wednesday at the Shenzhen Bay Sports Center with the clash between Spain and Kazakhstan.
Ukraine face Belgium on Thursday morning, before defending champions Italy take on China in the evening.
The Italians are seeking a third successive crown but their top singles player Jasmine Paolini is taking nothing for granted as the team prepare for a tough affair against the hosts, led by Olympic champion Zheng Qinwen.
"Qinwen, she played amazing in the US Open," Paolini told reporters on Tuesday.
"We expect really high level of tennis from her. I think also the support from the Chinese fans will be great for them.
"She's a great player. Very powerful. She can play really well on every surface. It's going to be a tough match. Hopefully I can play a great match and can be a great battle."