Katie Boulter and Heather Watson both won their opening singles matches to give Great Britain a 2-0 lead over Mexico in their Billie Jean King Cup play-off.
Boulter beat Marcela Zacarias 7-5 6-0 before Watson won 7-5 6-1 against Giuliana Olmos.
GB now just need to win one more rubber from the two reverse singles and doubles match on Saturday to secure victory in the tie.
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"Initially I was a little bit nervous," said world No. 291 Boulter. "Any match you play for Great Britain is a huge honour. I had the opportunity to do it today and I left it on the line and I got the job done and that is what matters.
"It was a really close first set and I managed to squeeze it through and that really helped me relax and so going into the second set I played some really good tennis. I've been playing some really good tennis in practice and I felt that when I settled I started to bring that out on the court."
If GB close out victory in the tie on Saturday they would be one win away from qualifying for the 2022 Finals.
GB have never won the Billie Jean King Cup, formerly known as the Fed Cup, but enjoyed a positive day at the National Tennis Centre in Roehampton.
Boulter was broken twice by world No. 206 Zacarias but fought back on both occasions and then broke again to take the opening set.
She swept through the second set in far more comfortable fashion and then watched Watson overcome Olmos in similar style.
After four breaks in the first five games of the match, Watson took her opponent's serve to secure the first set. Like Boulter, she then eased through the second set to seal the win.
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