Emma Raducanu beat Caroline Garcia of France 6-1 3-6 6-1 at Indian Wells to reach the third round.
The 19-year-old British number one raced into a 3-0 lead and, after saving four break points in the fifth game, impressively took the first set.
Garcia broke Raducanu three times on the way to levelling before the US Open champion cruised through the third set.
Fellow Briton Harriet Dart beat former world number three Elina Svitolina 2-6 6-3 6-3 to join her in round three.
The 12th-seeded Ukrainian broke the 25-year-old four times in the opening set before the British number three fought back to win the next two sets and claim victory in two hours 17 minutes.
Qualifier Dart, who is ranked 122nd in the world, faces Estonia’s Kaia Kanepi in the next round while Raducanu takes on Petra Martic of Croatia.
Raducanu, who is 13th in the world rankings, said it “means a lot to have come through” in three sets against former world number four Garcia.
“I thought the level of tennis was pretty high. It could have gone either way,” said Raducanu.
“She plays extremely powerfully and fast so as soon as I let up in the second set she climbed on top of it straight away.
“I knew I had to make some adjustments in the third set so I’m really happy that I was able to work that out in the match and come through a tough one.”
Raducanu was compromised by a blister when going out in the second round at the Australian Open, and had been able to play only four matches so far this year before facing world number 66 Garcia.
She also had to retire with a leg injury when playing Daria Saville in Guadalajara two weeks ago and there were doubts she would be fit to play in California.
However, Raducanu came through some testing moments against Garcia – in a match lasting one hour 31 minutes – before earning victory.
Meanwhile, Dayana Yastremska and her 15-year-old sister Ivanna were were beaten 6-1 6-1 by Irina Camelia-Begu and Monica Niculescu of Romania in the first round of the doubles competition.
The Ukrainian sisters were competing together for the second time since they fled their home city of Odesa last month following the Russian invasion of Ukraine.
Dayana, 21, who reached the singles final of the Lyon Open last week was knocked out in the first round of the singles event at Indian Wells on Thursday.