Jo Konta had earlier given Great Britain the lead with a 4-6 6-3 6-2 victory over Zarina Diyas but Boulter could not double the advantage, going down 6-3 2-6 7-6 (6-8) to Yulia Putintseva.
Kazakhstan's Yulia Putintseva celebrates winning her match against Great Britain's Katie Boulter
Image credit: Reuters
The reverse matches take place on Sunday at midday (BST) as Britain look to win promotion to World Group II for the first time in more than 25 years.
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And Boulter was gutted after the defeat left the tie in the balance.
"I put everything out there," Boulter said. "It's part of sport though - you win some and you lose some.
"It will be replaying in my head for a long time, that's for sure."
I am devastated, clearly.
"I will be doing my absolute best to recover tonight and I am sure my body will be fine. I was just struggling a little bit."
Boulter had a medical time out in the second set but recovered to go 4-0 up in the decider.
However, Putintseva clawed her way back into it and held off a match point in the final game before the breaker.
Boulter squandered two more opportunities at 6-4 and 6-5 on her serve in the tie-break before finally being overcome.
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