Johanna Konta was the heroine for Great Britain after she fought through exhaustion to beat Aleksandra Krunic of Serbia 7-6(1), 3-6, 6-2 - and seal a place in the Fed Cup World Group II playoffs.
The British No.1 sank to the floor at the end of the second set and again after match point, and was visibly emotional - but was able to join her team-mates in their celebrations.
Katie Boulter had earlier put Team GB on the brink of victory by beating Ivana Jorovic 6-4, 6-3.
Russia also secured their place in the playoff - scheduled for April - by beating Sweden, rounding off an undefeated week in Poland thanks to dominant singles displays from Natalia Vikhlyantseva, who beat Johanna Larsson 7-6(1), 6-2, and Anastasia Pavlyuchenkova, who defeated Rebecca Peterson, 6-3, 6-2.
It was a tighter encounter in Astana, as Kazakhstan progressed against China thanks to a doubles win for Anna Danilina and Galina Voskoboeva, 7-5, 6-0 over Yang Zhaoxuan and Zheng Saisai.
Earlier in the day, Zarina Diyas had beaten Zheng 6-3, 6-2 in the singles before World No.40 Zhang Shuai beat Yulia Putintseva 6-3, 4-6, 6-4 to level things up.