Ukraine, forced to play their home ties on neutral ground, had been comfortably 2-0 ahead overnight in Florida against a Romania side missing top player Sorana Cirstea as well as former Wimbledon and French Open champion Simona Halep.
However, Ana Bogdan claimed a 6-4, 4-6, 6-3 victory over top 20 star Elina Svitolina despite trailing 2-0 in the deciding set. Ranked 64, she battled back, winning a 20-point game and then serving out the match with ease.
"I gave my heart out there," said the 31-year-old.
Jacqueline Cristian then levelled the tie at 2-2 with a come-from-behind 2-6, 6-4, 6-4 win over veteran Lesia Tsurenko.
With the balance of power shifting, Bogdan and Cristian defeated twin sisters Lyudmyla and Nadia Kichenok 6-2, 7-6 in the deciding doubles to secure a dramatic 3-2 victory and a debut place in the finals in November.
'OK for me to win'
Japan also made the finals by seeing off Kazakhstan in Tokyo with Nao Hibino sealing the victory thanks to a hard-fought 6-4, 3-6, 7-6 win over world number 50 Yulia Putintseva.
Four-time major winner and former world number one Naomi Osaka sat out Saturday's action having helped set Japan on their way to a 2-0 lead in the best-of-five series on Friday with victory over Putintseva.
Osaka was playing in the tournament for the first time since 2020 having missed all of last year to give birth to her first child.
"I started wondering if it was OK for me to win my match - there were a lot of fans looking forward to watching Osaka," joked world number 79 Hibino.
"It was mixed emotions but I really wanted to clinch the win."
Emma Raducanu, plagued by back, wrist, stomach and ankle injuries since her 2021 US Open title, defeated Diane Parry 4-6, 6-1, 7-6 to secure victory for Britain over France at Le Portal.
Raducanu, whose ranking has plunged to 302 in the world, had already defeated French number one Caroline Garcia on Friday as the two sides were locked 1-1 overnight. Katie Boulter then nudged Britain in front on Saturday by beating Clara Burel 7-5, 6-0.
The victory was Britain's first on clay since April 2007.
"The players have done it, the team have worked together really well, and we deserve our spot in the finals. That's where I believe this team belongs," said Britain skipper Anne Keothavong.
World number one Iga Swiatek defeated Swiss 18-year-old Celine Naef 6-4, 6-3 to send Poland, 2-0 ahead overnight in Biel, back to the finals.
Swiatek reeled off six straight games to lead 6-4, 4-0, putting her team on the brink of sweeping 2022 champions Switzerland. Naef, ranked 148, got back on serve at 4-3 but four-time major champion Swiatek raced away with the next two games for victory.
Pegula in hurry
World number five Jessica Pegula needed just 51 minutes to defeat Hanne Vandewinkel 6-2, 6-0 as the United States, the 18-time champions, claimed victory over Belgium in Florida.
"I think everybody here can see the level that Jess is capable of," said US skipper Lindsay Davenport after seeing her top player fire 21 winners past the 19-year-old Belgian.
Seven-time champions Australia surged into the finals with a victory over Mexico in Brisbane, handing Samantha Stosur a winning start to her reign as captain.
Taylah Preston, just 18, swept past the experienced Marcela Zacarias, 12 years her senior, 6-1, 6-1.
In Bratislava, 16-year-old Australian Open junior champion Renata Jamrichova secured Slovakia's win over Slovenia. The teenager beat world 203 Veronika Erjavec 6-2, 6-0.
Two-time champions Germany edged out Brazil 3-1 in Sao Paulo when Laura Siegemund saw off Carolina Alves in three sets.
The eight winning countries advance to November's 12-team finals in Seville where they join hosts Spain, defending champions Canada, 2023 runners-up Italy and wildcard Czech Republic.
