Great Britain battled hard to defeat the Netherlands 2-1 in their second Fed Cup Euro/Africa Zone Group I match.
British number two Anne Keothavong lost 6-3 6-7 (3-7) 6-3 to Bibiane Schoofs.
Elena Baltacha responded from being a break down in the second set to beat Michaella Krajicek 6-3 6-3 before doubles duo Heather Watson and Laura Robson secured victory 7-5 7-6 (7-5).
"I am absolutely delighted and very, very proud of them - it was a fantastic day," captain Judy Murray said.
Great Britain need to win their group if they are to qualify for the World Group play-offs and Baltacha remains confident they can achieve that.
"Today was a result of all the work that the team have put in behind the scenes," she said.
"All the analysis that Judy has been helping us with has helped enormously.
"As for the overall team win, well, what can I say? I'm so proud of our team. The girls all did brilliantly and we're just so excited."
Great Britain had won their first Group C match against Portugal on Wednesday 3-0.
They will now play Israel in their third and final match on Friday at 1400 GMT, seeking the win which will make sure they finish top of their pool and earn them a place in Saturday's promotion play-offs.
The format sees 15 nations form four round-robin pools, played from Wednesday to Friday. The nations that finish top in each pool will go through to the promotion play-offs.
The two winning teams will go through to the World Group II play-offs, while the bottom nations contest the relegation play-offs to decide which two teams are relegated to Euro/Africa Group II.