World number 10 Rybakina blitzed past Yuliana Lizarazo at Pat Rafter Arena in Brisbane 6-1, 6-2 in only 55 minutes to improve her singles record to 9-1 at the event, which was previously known as the Fed Cup.
Putintseva was even more ruthless against 18-year-old Valentina Mediorreal, who endured a horror tournament debut in a 6-0, 6-1 drubbing over just 37 minutes.
Such was the world number 23's dominance that Mediorreal won just 14 points, and only three on her first serve.
"We're super happy and excited to play (the finals) in Shenzhen," said former Wimbledon champion Rybakina.
"We had great support and the president of our association was here, so really nice to be here all together.
"We were focusing of course on singles to get the wins... super happy to get them in such a competent way."
Zarina Diyas and Zhibek Kulambayeva then overcame Lizarazo and Maria Paulina Perez-Garcia 6-2 5-7 6-4 in the doubles match to complete the whitewash.
The victory ensured Kazakhstan, who beat Australia 2-1 in their opening Group D tie on Thursday, booked their spot at the September finals alongside hosts China and defending champions Italy.
Colombia and Australia, who meet in a dead rubber on Saturday, now move to the play-offs in November along with the best performers from the 2025 regional Group I events.
Those play-off winners will earn their place in the 2026 qualifiers.
Canada got off to a superb start in Group A in Tokyo, as the 2023 champions took a 2-0 advantage over Romania thanks to wins by Victoria Mboko and Marina Stakusic.
In other ties, Spain meet Brazil in Group B in Ostrava, Slovakia play Denmark in Group C in Bratislava and Britain take on Germany in Group F in The Hague.
