Mayer ousted third-seeded David Ferrer 6-4, 6-3, Almagro was a three-set winner over fourth-seeded Tomas Berdych and Monfils beat No. 5 Roger Federer for just the second time in eight tries with a 6-4, 6-7 (5-7), 6-3 win.
Mayer swept past Ferrer with four breaks, with three coming in the second set. Mayer saved three of Ferrer's four break chances. He lost just 10 points on serve in the first set.
Almagro edged Berdych 6-7 (6-8), 6-3, 7-6 (7-4) in a 212-point match that took more than 2 1/2 hours. Almagro took nearly three-quarters of the points on serve and lost his serve just once.
Federer was playing from behind much of the day Thursday, having to come back from a 3-5 deficit in the second set and winning the final four points of the tiebreaker. But Monfils posted a break in the fourth game of the third set and held on from there.
Top-seeded Novak Djokovic won almost 80 percent of the points on serve in a 6-3, 6-3 win over Fabio Fognini while second-seeded Rafael Nadal came away with a 6-1, 7-6 (7-5) decision over Carlos Berlocq without facing a break point.
Also Thursday, No. 7-seeded Jo-Wilfried Tsonga beat 12th-seeded Kei Nishikori, ninth-seeded Stanislas Wawrinka topped No. 10 Milos Raonic 7-6 (7-2), 6-4 and sixth-seeded Juan Martin del Potro advanced to the quarterfinals when 11th-seeded Tommy Haas was unable to play because of a back injury.