British number one Heather Watson withstood a storming fightback from Camila Giorgi to reach the third round in Indian Wells for the first time.
Watson, 22, looked on course for a straightforward win at 5-0 in the second set, only for the Italian 29th seed to win five straight games.
The Briton held her nerve, however, and sealed a 7-5 7-5 victory with her sixth break of serve in the match.
Watson goes on to face seventh seed Agnieszka Radwanska in the last 32.
"It was a very tough match as I knew it would be," said Watson. "Camila's a great player and she's shot up the rankings this past year."
Giorgi, ranked 10 places higher than Watson at 33 in the world, hit 18 double faults and 54 unforced errors in a wildly inconsistent performance.
The Italian twice went a break up in the first set but the constant flow of double faults allowed Watson to recover each time, and ultimately take it in the 12th game.
Watson was in total command as she reeled off 11 consecutive points early in the second and made it seven games in a row to lead 5-0.
Radwanska has won all three previous matches against Watson, most recently in Indian Wells last year
With the match all but gone and the pressure off, Giorgi suddenly found her game and hauled her way back against an increasingly edgy Watson.
The Guernsey-born player was under huge pressure at 5-5, 30-30, but found an ace at the crucial moment and then broke for the sixth time to seal the win.
"I didn't feel I did much wrong [in the second set], she played too good, hitting winners and aces. I just had to stay tough and keep fighting," added Watson.
"I feel that I'm playing better and better as each match goes on and hopefully I can play even better in my next match."
Poland's Radwanska beat American Alison Riske 6-3 6-1, while Romanian third seed Simona Halep overcame Russian's Daria Gavrilova 2-6 6-1 6-2.