Johanna Konta reached round three of the Miami Open but fellow Briton Kyle Edmund was beaten by Novak Djokovic.
Konta, the 24th seed, saw off Montenegro's Danka Kovinic 6-4 6-2 to set up a third-round meeting with Russian qualifier Elena Vesnina.
The British number one lost her opening service game, but there were no further alarms as she broke world number 51 Kovinic four times over one hour and 24 minutes.
"It was much closer than the second set score showed," said Konta. "We had a lot of deuce games, a lot of back and forth.
"She's been pushing some of the best players in the world to quite the limit in the last couple of weeks, so I was really happy how I was able to compete against her."
Vesnina beat Venus Williams in three sets, and will look to repeat her victory over Konta from their only previous meeting four years ago.
Konta said: "I actually saw her in the locker room and asked her 'who do you play next', and she said, 'Oh, you!'
"I've played her I think only once before - I definitely lost to her that time. I'm definitely looking forward to the challenge."