Venus Williams will face British number one Johanna Konta in the Miami Open fourth round.
The 37-year-old world number eight defeated 26-year-old Kiki Bertens, of the Netherlands, after saving three match points.
Williams came back in style against world number 29 Bertens, winning 5-7 6-3 7-5.
The American raced to a 5-0 lead before losing the next seven games and the first set.
She then won the second set comfortably before an exciting decider that saw Bertens take a 4-1 lead.
Bertens was suffering from cramp in her right arm in the latter stages of the match and appeared to be in tears at one stage.
There were five breaks of serve in the final set before Williams completed her victory.
"I’m not sure how I did that," Williams said. "I had a lot of chances, she had a lot of chances.
"It didn’t look good sometimes but that’s why you play to the last point. We were in a battle but I’m happy to be coming back tomorrow."
Defending champion Konta, ranked 14th in the world, secured a 6-2 6-1 victory over Elise Mertens in 65 minutes.
Konta was helped in the first set by Mertens registering six double faults – including four in one game – and she played an almost perfect match as she swept into the last 16.
"I tried to take my game to her and managed to do that for big pockets of time, but it’s never easy to come through so I’m really happy," Konta said.
"I definitely have a great relationship with this tournament, the biggest title of my career has come here. Hopefully I can get to the end again."
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