Angelique Kerber displayed her grit and vaunted fitness as she battled back to beat France’s Pauline Parmentier 7-5 3-6 7-5 in scorching heat on Monday to reach the fourth round of the BNP Paribas Open.

Kerber was joined in the round of 16 by Venus Williams.

The 36-year-old American, who was forced to saved three match points in her opening victory, faced no such drama on Monday with a 6-4 6-2 victory over Lucie Safarova of the Czech Republic.

Kerber, who will reclaim the world No.1 ranking next week, won the first set by taking the last three games after facing set point, and was a point from trailing 5-2 in the third set before surging to victory.

“It was a tough match and a high-level match from both of us,” the second-seeded German said on court after her two-hour, 33-minute victory. “Pauline played unbelievably from the first ball, and we both battled until the end.”

Kerber persevered despite Parmentier saving 13 break points in the match.

“She is a really tricky opponent,” the German said. “She played a lot of spin, especially from the forehand side.

“I’d had great practices in the last few months so I’m ready to stay on court for three hours.”

Next up for Kerber will be 14th-seeded Russian Elena Vesnina, who recovered from a bout with dizziness to beat 25th seed Timea Babos of Hungary 6-4 1-6 6-4.

Fourth seed Simona Halep met a different fate against her French opponent, as 28th seed Kristina Mladenovic registered a 6-3 6-3 win to reach the fourth round.

Mladenovic, riding a positive wave after notching her maiden WTA title at St Petersburg and reaching another final at the Abierto Mexicano Telcel, maintained her form against a rusty Halep.

The Romanian, playing her first event in five weeks due to a knee injury, fell in one hour 42 minutes.