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.
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.