Johanna Konta and Heather Watson continued their fine Fed Cup form to send Great Britain through to the World Group II play-offs for the second straight year.
After topping their group in the Europe/Africa Zone, Konta and Watson both posted their third straight victories to give Britain an unassailable 2-0 lead in their play-off against Hungary.
The victory means Anne Keothavong’s side are one step away from the tournament’s elite for the fourth time in the last seven years.
They have fallen short on the previous three occasions, losing away ties to Sweden in 2012, Argentina the following year and Romania last year, when Ilie Nastase’s shocking behaviour overshadowed a 3-2 victory for the hosts in Constanta.
Their opponents will be one of the losing teams from this weekend’s World Group II first-round ties, and the primary hope for Keothavong’s side will be that they are drawn to play at home, having not done so since 1993.
Britain have been favourites in all the rubbers they have played in Tallinn, with the clash between Konta and Anett Kontaveit of Estonia on Friday the only one where there appeared any real danger.
Watson found 19-year-old Dalma Galfi, ranked 265, a step up from her previous opponents and had to come from a set down to win the opening rubber 3-6 6-1 6-4.
Konta was up against another 19-year-old in Fanny Stollar, ranked 209, and, although the world number 11 did not have things all her own way, she ultimately eased to a 6-3 6-1 victory to seal victory for Britain.