Katie Boulter had put Great Britain 1-0 up in the tie earlier in the dayFed Cup 2019Venue: University of Bath Dates: 6-9 February 2019Coverage: BBC website will have live text commentaries on selected GB matches from 16:30 GMT on Wed-Fri.
Johanna Konta held her nerve to secure victory for Great Britain over Slovenia in their first home Fed Cup tie for 26 years.
Britain's world number 39 saved three set points in a tense first-set tie-break, before eventually beating Dalila Jakupovic 7-6 (9-7) 6-2 in Bath.
Katie Boulter had given GB a winning start by overcoming Kaja Juvan 6-4 6-2.
It meant GB had an unassailable lead before Harriet Dart and Katie Swan won the doubles rubber for a 3-0 victory.
GB, who are bidding to reach the World Group II play-offs for a third consecutive year, face Greece in their next Group A match on Thursday (from 16:30 GMT).
There are eight teams - split into two groups - taking part in the Europe/Africa round-robin event in Bath between Wednesday and Saturday, with only one side able to progress to April's play-off event to fight for promotion to the second tier.
In the absence of the experienced Heather Watson, who was ill, debutant Dart and Bristol-born teenager Swan entertained the West Country crowd with a 6-2 6-2 win over Jakupovic and Juvan.
They received rapturous support throughout the evening despite a relatively late 22:15 GMT finish.
Great Britain are being well supported by sell-out crowds for their sessions in Bath'Ultimate pro' Konta seals victory
It took Konta an hour and 20 minutes to win a gripping first set against 27-year-old world number 86 Jakupovic.
There were eight breaks of serve and Konta saved three set points by winning four points in a row in the tie-break before slamming a forehand on to the outside edge of the line to claim the set.
She produced a more commanding performance to take the second set, wrapping up victory on her third match point when Jakupovic netted a service return.
"What I tried to draw on is vast experiences - it's not the first time I've been down in a tie-break or down in a set," Konta told BBC Sport.
"I tried to stay calm because there was every reason for me to be calm. I thought I was competing well. I just tried to trust that more than anything else."
GB captain Anne Keothavong added: "Jo did a great job to come through that first set. It wasn't easy but Jo is the ultimate pro."
Boulter races to swift win
Earlier, Leicester-born Boulter, who is at a career-high singles ranking of 83 in the world, dominated her rubber against 18-year-old Juvan, cheered on by a sell-out crowd at the University of Bath's Sports Training Village.
Her victory in one hour two minutes was 18 minutes quicker than Konta's first set.
"Being here is quite tremendous. Everyone showed so much support out there," said Boulter, who was making her singles debut in the Fed Cup.
"I had a great team around me to help me with those nerves and put me in the right place mentally."
Watson misses out with illness Harriet Dart and Katie Swan's victory in the doubles meant GB were the only team to win all three of their matches on day one in Bath
British singles number three Watson was ruled out of Wednesday's tie through illness, paving the way for 22-year-old Dart to pair up with 19-year-old Swan in the doubles.
Watson, who was replaced by Boulter as British number two last month, is the most experienced member of the team with 31 Fed Cup appearances compared to 20 for Konta.
Keothavong said she was "hopeful" Watson would recover in time to play this week but did not give details of the illness.
"She was on the practice court with us yesterday and we thought she was getting better but it wasn't the case," she said.
"So she just needs time to recover and get herself in the best shape possible. She's still very much part of this team. She's desperate to play a part in this home tie."
While the tie had already been won, the result of the doubles rubber could still be important in the final standings if teams are level.
How did the other teams do?
In Group A's other matches, Hungary won their tie with Greece 2-1 with Dalma Galfi and Reka-Luca Jani beating Maria Sakkari and Despina Papamichail 6-3 6-4 in the decisive doubles rubber.
In Group B, Croatia - led by the highest ranked singles player at the event with world number 25 Donna Vekic - beat Turkey 2-1, and Serbia beat Georgia 2-1.
On Saturday, the group winners will face each other to decide who will progress from Bath to April's World Group II play-offs.
Great Britain - ranked 18th in the world - are the favourites to top Group A, as they bid to end their long wait for a return to the second tier, having been outside the World Group since 1993.
