Elena Baltacha and Anne Keothavong won their singles to secure an unassailable 2-0 lead before Keothavong and Sarah Borwell teamed up to win the doubles.
Britain, who beat Hungary on Wednesday, will finish top of Group A if they see off Luxembourg on Friday.
That would mean a place in Saturday's promotion play-offs against another group winner.
The victor in that tie will reach the World Group II play-offs in April.
Baltacha, the world number 108, got Britain off to a perfect start against Holland with a 6-2 6-4 victory over Michelle Gerards.
British number one Keothavong, ranked 54th in the world, had a slightly tougher time against talented 18-year-old Arantxa Rus before triumphing 6-4 6-4.
Keothavong returned to partner Sarah Borwell to a comfortable 6-4 6-0 win over Nicole Thyssen and Pauline Wong.
"I'm pleased with another emphatic victory," said British captain Nigel Sears.
"It's a good feeling to be leading the group after two days but we know we still have work to do if we are going to top the group and gain a place in the semi-finals.
"The team is in great shape and we are looking forward to tomorrow's match against Luxembourg."
Britain are yet to drop a set in Tallinn.
Baltacha posted a 7-5 6-3 win over Greta Arn in Wednesday's 3-0 win over Hungary, before Keothavong defeated world number 25 Agnes Szavay 6-3 6-2.
Borwell and Mel South made it a 3-0 whitewash with a 6-4 6-3 win over Szavay and Katalin Marosi in the doubles.
Britain's women are enjoying an encouraging run of form, with South joining Keothavong in the top 100 this week and Baltacha rising to 108th on the back of a second-round appearance at the Australian Open.
Elsewhere, Jelena Dokic made a triumphant return to Australia's Fed Cup team as they beat South Korea 3-0.
Dokic beat Lee Jin-a 6-0 6-3 in less than an hour on her first Fed Cup appearance for Australia since 2000 following the well-publicised fall-out between her estranged father Damir and the country's tennis officials.
Dokic's last Fed Cup appearance was for her native Serbia and Montenegro in 2004.Source : http://news.bbc.co.uk/sport2/hi/tennis/7870855.stm