Baltacha and Borwell won both their doubles matches together
Great Britain beat Belarus 2-1 in their final Fed Cup group game but it was not enough to win Europe/Africa Group 1.
In her second match back after six months out with a knee injury, former British number one Anne Keothavong beat Ekaterina Dzehalevich 7-6 (9-7) 6-1.
Defeat followed for Katie O'Brien before doubles pair Elena Baltacha and Sarah Borwell won a dramatic doubles.
Britain beat Bosnia-Hercegovina on day one but lost to Austria on Thursday, ending their hopes of progressing.
Keothavong, ranked 127th, had suffered a 6-2 6-2 defeat by Austria's Patricia Mayr on Thursday but got back to winning ways against Dzehalevich.
Belarus, who had already been eliminated following two defeats, called up the world number 156 after sixth-ranked Victoria Azarenka fell ill.
It was an amazing performance
Keothavong saved two set points in the first set tie-break before easing away to win in straight sets.
"I'm glad I got through that and it's nice to get my first win after so long out of the game," said the Londoner. "It is just such a pleasure to be out there on the court - it really is.
"After I got through the first set I loosened it up and started hitting a bit more freely and gained a bit of confidence.
"Those are the kind of matches I need - these next few months are going to be tough for me, but this is a start."
O'Brien, ranked 83rd, then lost 6-3 6-3 to world number 55 Olga Govortsova in the second singles match before Govortseva and Tatiana Poutchek took on Baltacha and Borwell.
The Belarusian team looked set for victory when they led by a set and 3-0 but two match points went begging at the end of the second set, and the Britons fought back to win 3-6 7-5 6-2.
"It was an amazing performance," Borwell told the LTA website. "It's always good when you bring a match back from the brink of match points down.
"Just the energy Bally brings to the court is great and I'm pretty much the same, so it was a lot of fun - I really enjoyed it."
Great Britain will play the Netherlands on Saturday to decide their final placing, which affects the seedings for next year, while Austria go through from Group D to the weekend's play-offs, with two places in World Group II up for grabs.