South cruised through her first singles match of the week
Great Britain's Fed Cup team are one step away from the World Group II play-offs after a 3-0 victory over Luxembourg in Tallin, Estonia.
Britain have won Group A of the Europe/Africa Zone and will play another group winner on Saturday for the right to take part in April's play-offs.
Mel South, playing her first singles of the week, beat Fabienne Thill 6-0 6-2.
British number one Anne Keothavong followed up with an emphatic 6-1 6-2 victory over Mandy Minella.
South, who recently broke into the world's top 100, was due back on court with Sarah Borwell for the doubles against Thill and Minella, but they were given a walkover.
Britain also whitewashed Hungary and Holland on their way to topping the group.
Captain Nigel Sears said: "We wanted to finish things up properly to win the group in style and the girls certainly did that.
"I'm very happy with their performances in every match and they really deserve this opportunity to play for a promotion spot."