Boulter came from a set and a break down to beat Diyas 6-7 (1-7) 6-4 6-1, giving Britain an unassailable 3-1 win.
Boulter trailed by a set and a break - and was troubled by a back problem - before beating Diyas 6-7 (1-7) 6-4 6-1.
Fed-Cup Singles
Barty beats doubles partner Azarenka to level Fed Cup semi-final
20/04/2019 AT 09:00
Johanna earlier Konta gave Great Britain a 2-1 lead in their Fed Cup World Group II play-off against Kazakhstan after a 4-6 6-2 7-5 victory over Yulia Putintseva.
Konta fought back from a set down to level the match only to be 4-1 down in the decider - not helped by the umpire handing her a time violation on break point in the decider.
"I was so nervous watching Katie on the side of the court," said Konta after.
"I'm sweating so much. We have been in this position for the last three years in a row.
I am almost speechless which is not normal.
But Putintseva was broken when attempting to serve out the match as sublime striking of the ball from Konta in the final few games ensured the British No 1 secured the win.
"Ah, finally! I'm ecstatic for the team," said Britain captain Anne Keothavong told the BBC.
"It was such an incredible effort. We kept putting ourselves in this position. But I really feel that having the home advantage this time around made a big difference."
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Laver Cup
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