British number one Johanna Konta had to dig deep to join compatriot Heather Watson in the Miami Open last 16.
Konta, the 24th seed, recovered from a sluggish end to the opening set to beat Russian qualifier Elena Vesnina 4-6 6-1 7-6 (7-3) in two hours and 23 minutes.
The Briton looked to have weathered the storm when she went a break up in the third set but Vesnina fought back.
Konta twice had to serve to stay in the match but held her nerve before taking control of the tie-break.
She will face 32nd seed Monica Niculescu of Romania in the fourth round.
Konta keeps cool in Miami heat
Vesnina was playing her fifth match of the week having come through qualifying, and beat Venus Williams in the previous round, but Konta proved just the stronger.
On another day of punishing heat and humidity, the pair wore ice towels at the changeovers and left the court to freshen up before the final set
"The heat rule was in but we didn't take the break. We needed to change our clothes because they were so heavy with sweat," Konta told BBC Sport.
The British number one played three brilliant points from 6-5, 30-15 down in the decider, and reeled off four straight points to clinch the tie-break.
"She was playing a very good level and has been for the last number of weeks," Konta added.
"I knew going into the match there wasn't going to be much in it either way, so I was very happy I was able to stay calm, kept fighting and come through it in the end."
Britons set for manic Monday
Konta's victory made it three British players through to the last 16 of the singles in Miami, with all three in action on Monday.
Heather Watson will play Simona Halep at 16:00 BST, before Konta takes on Niculescu and Andy Murray faces Grigor Dimitrov, with both those matches at approximately 20:00 BST.
"I think it's a great achievement for British tennis, and also at home to be able to promote this great sport," said Konta.
"Also Jamie Murray is number one in the world - gosh, I'm so happy. I saw that when I came off court and that made my day.
"I'm so happy for him. That's an incredible achievement."
Djokovic eases through
In the men's tournament, Novak Djokovic remained relatively untroubled as he moved into the last 16 with a 6-4 6-1 win over Joao Sousa.
Spain's David Ferrer was knocked out, however, as he lost 6-7 7-6 7-5 against France's Lucas Pouille.