Serbian fifth seed Dusan Lajovic fought back from a set down to triumph over Benoit Paire in the Argentina Open first round while Spanish veteran Fernando Verdasco also progressed on Monday.
Lajovic, who is currently ranked 37th in the world, beat 50th-ranked Paire 4-6 6-4 7-6 (7-3) in just over two hours in Buenos Aires.
In a tight match, the Serbian got the edge in the third-set tiebreak as his first serve seldom let him down.
Former top 10 player Verdasco, now 38-years-old, defeated Bolivian Hugo Dellien 6-4 3-6 6-1 in two hours and two minutes.
Serbian eighth seed Laslo Dere got past compatriot Miomir Kecmanovic 6-4 1-6 6-1, while Argentine pair Federico Coria and Francisco Cerundolo also progressed.
Meanwhile at the Dallas Open, veteran South African Kevin Anderson proved too good for Sam Querrey 6-4 6-4.
The 35-year-old former US Open and Wimbledon finalist sent down 21 aces as he won in little over an hour.
Emerging American Brandon Nakashima defeated Australian John Millman 7-5 7-6 (7-3) in the first round.
Keys downs Gauff to reach Madrid Open quarter-finals
Madison Keys is through to the quarter-final of the Madrid Open for the first time in her career after rallying to a 7-6 (7-4), 4-6, 6-4 win over Coco Gauff on Monday.
The 29-year-old trailed 5-2 in the first set and 4-2 in the third set but rallied in both to come from behind to beat the number three seed.
Despite winning the second set, Gauff struggled to find her rhythm, suffering from 13 double faults, including two in the final game.
Keys will face former Madrid Open champion Ons Jabeur for a spot in the semi-final after the number eight seed overcame Jelena Ostapenko in straight sets.
Data debrief: Keys reaches new milestone
Having lost in the first round in seven of her nine previous trips to the Spanish capital, Keys has now bettered her previous best finish in Madrid - a third-round showing in 2016.
Keys hadn't won three matches in a row since reaching the US Open semifinals last year.
Keys downs Gauff to reach Madrid quarter-finals
Madison Keys is through to the quarter-final of the Madrid Open for the first time in her career after rallying to a 7-6 (7-4), 4-6, 6-4 win over Coco Gauff on Monday.
The 29-year-old trailed 5-2 in the first set and 4-2 in the third set but rallied in both to come from behind to beat the number three seed.
Despite winning the second set, Gauff struggled to find her rhythm, suffering from 13 double faults, including two in the final game.
Keys will face former Madrid Open champion Ons Jabeur for a spot in the semi-final after the number eight seed overcame Jelena Ostapenko in straight sets.
Data debrief: Keys reaches new milestone
Having lost in the first round in seven of her nine previous trips to the Spanish capital, Keys has now bettered her previous best finish in Madrid - a third-round showing in 2016.
Keys hadn't won three matches in a row since reaching the US Open semifinals last year.
Nadal goes the distance to reach Madrid Open last 16
Rafael Nadal battled to victory over three hours on the court against Pedro Cachin at the Madrid Open on Monday to seal a 6-1 6-7 (5-7) 6-3 win to reach the last 16.
The former world number one looked back to his best as he cruised through the opening set but was pushed hard in the second by Cachin.
Nadal came from behind to level at 5-5, but Cachin eventually sealed the set on his third set point.
The Spaniard then rallied in the third set, cutting down on his errors to regain control and advance to the fourth round at a tour-level event for the first time since 2022.
Nadal is one step away from booking his place in a 10th consecutive quarter-final in Madrid and will face Jiri Lehecka on Tuesday in the next round after the 30th seed overcame Brazilian qualifier Thiago Monteiro in two sets.
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