The 22-year-old, making her singles debut in the team competition this week, beat Serbia's Ivana Torovic 6-4 6-4 to put Great Britain 1-0 up in the best-of-three tie, with the winner sealing qualification to the World Group II play-off in April.
Boulter will now watch as Johanna Konta tries to seal the win against Aleksandra Krunic and, if that result goes against GB, get ready for a potential deciding doubles rubber.
Boulter has put in a supreme physical effort, having won two three-set thrillers earlier in the week, and says the achievement of racking up four successive victories in front of a home crowd is a potential career highlight.
"It's definitely up there," she said. "Considering it was my debut as well, it's going to be one I'm going to remember, that's for sure.
"It makes it so special. I came into this week not knowing what to expect and to start my debut and come out with four wins is probably better than I ever imagined.
"I'm really happy that today went well.
"Anything is possible, I wasn't going into this week thinking I am going to win four matches, I was just leaving my heart on the line and doing the best that I can and see what happens."
Boulter was dominant throughout against Torovic, having won the first three games, but she also showed her fighting spirit in the second set as she saved four break points in a crucial eighth game that set up the win.
And the world number 83 will have been delighted to get the job done in straight sets against a player ranked 34 places below her, given she had spent over five-and-a-half hours on court in her previous three wins.
"I mean without a doubt this week is going to be a little bit stressful," she added. "I'm doing the best I can every single week of the year, but playing for your country is a little different than just playing for yourself.
"I'm trying to do people proud. It always has a toll on your body no matter what, I feel I've done really well this week with the recovery. I'm feeling as good as I can right now."
