Watson got the ball rolling with a straight-sets victory over Jelena Ostapenko, the British No3 edging a tight opening set 7-5 before blowing her opponent away 6-1 in the second.
“It was a very tough match,” Watson said. “She’s a young, dangerous player.
“She’s a top junior and got to the quarter-finals in the juniors at the Australian Open. She’s a strong girl for only 16 years old.”
Konta then took on Diana Marcinkevica and having taken the opening set 6-3 she then lost the second 6-4 and found herself 5-2 down in the decider.
But she reeled off five consecutive games to take it 7-5 and give Britain their first victory in this year’s competition.
Jocelyn Rae teamed up with Watson for the concluding doubles match but lost to Diana Marcinkevica and Jelena Ostapenko 6-3 6-7 (4-7) 7-6 (7-5).
Britain are just one of 17 nations competing in Budapest for a play-off tie in the Fed Cup World Group II, with the first phase being a round-robin format where Judy Murray’s team have been drawn in Group B.
The team, which consists of Watson, Konta, Tara Moore and Rae, will next face Romania on Friday followed by hosts Hungary on Sunday.
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