Johanna Konta fought back from 4-1 down in the deciding set to beat Yulia Putintseva and put Great Britain 2-1 ahead in their Fed Cup play-off tie with Kazakhstan.
The British number one won 4-6 6-2 7-5 in two hours and 25 minutes at London's Copper Box Arena.
Konta was broken twice in the first set but responded to dominate the second.
She then won six of the last seven games in the decider to complete a sensational comeback.
If Katie Boulter beats Zarina Diyas in the second singles rubber later on Sunday, Britain will gain promotion to World Group II - a level they last played at in 1993.