Johanna Konta and Heather Watson both won as Britain beat Hungary to reach the Fed Cup World Group II play-off.
World number 11 Konta broke Fanny Stollar's serve five times in a 6-3 6-1 win to give GB an unassailable 2-0 lead with just the doubles rubber to follow.
Earlier, Watson came from a set down to beat Dalma Galfi 3-6 6-1 6-4.
The British number two was broken in the eighth game of the deciding set after wasting two match points, but held her next service game to win.
After topping their group in the Europe/Africa Zone, Konta and Watson won their third successive matches in Estonia to put Anne Keothavong's team into April's World Group II play-offs for the second straight year.