Konta needed to reply for Britain after Heather Watson was beaten in straight sets by rising star Naomi Osaka in the opening rubber.
Konta was able to do that with a comfortable victory over Kurumi Nara to set the tie up for an enthralling encounter between her and Osaka in the third rubber in the early hours of Sunday morning.
The British number one got off to a flying start and broke her opponent’s serve in the opening game, only to be forced to save three break points herself before holding to take a 2-0 lead.
Konta needed a second serve ace to hold in game four for a 3-1 lead, before having to work hard again to win game eight and take a 5-3 lead, forcing Nara to serve to stay in the first set.
Nara was able to do that but Konta came through when she finally took the next game on a fourth set point to win the opener 6-4 when Nara hit a forehand wide.
Nara made a slow start to the second set as she suffered her second service break of the match in the opening game, a powerful backhand return giving Konta a second break point which she took as her opponent double-faulted.
Konta dug deep to save two break points on her own serve in game two before an ace earned her a 2-0 lead as the second set looked like a repeat of the first.
Konta upped the pressure in game three to claim a second break for a 3-0 lead, only for Nara to break back in game four. But Konta broke again to lead 5-2 and then served out for a 6-4 6-2 victory to level the tie at 1-1.
That win set up a meeting with Osaka, a player Konta has a 3-0 lead over in their previous meetings.
Osaka made short work of Watson with a 6-2 6-3 win to make it five wins from as many Fed Cup matches for the Japanese player.
A strong forehand from Oasaka gave her a break in game four of the opening set and a second break handed her the set.
Osaka also broke in game four of the second set to lead 3-1 and looked poised to take the match when serving at 5-3 only to have to save two break points before claiming the win.
In Sunday’s reverse singles Watson will face Nara and there will be a doubles match featuring Anna Smith and Gabi Taylor if necessary.