Stan Wawrinka set up a clash with Roger Federer at the Indian Wells Masters, while Rafael Nadal and Marin Cilic advanced on Sunday.
Federer and Nadal were untroubled at the ATP 1000 event, the former champions progressing with straight-sets victories.
Cilic was also relatively comfortable, while Wawrinka was pushed before getting through in three sets.
On what was a relatively good day for the seeds, Kei Nishikori and John Isner were also among the winners.
FEDERER, NADAL CRUISE
A five-time champion at Indian Wells, Federer outclassed Peter Gojowczyk 6-1 7-5 in just 77 minutes.
Federer has reached at least the final of the event in five of the past seven years, and he had no problems against Gojowczyk.
A tougher test awaits in the third round in Wawrinka, who got past Marton Fucsovics 6-4 6-7 (5-7) 7-5 in a clash lasting almost three and a half hours.
Nadal was in a ruthless mood, the Spanish star and three-time champion crushing wildcard Jared Donaldson 6-1 6-1.
JOBS DONE FOR CILIC, NISHIKORI
Cilic was relatively comfortable during a 6-3 6-4 win over Dusan Lajovic.
The Croatian 10th seed converted just four of 15 break points but still progressed in straight sets.
Nishikori was pushed in his second-round meeting with Adrian Mannarino, edging through 6-4 4-6 7-6 (7-4).
Isner, the American eighth seed, was on court for less than an hour, crushing Alexei Popyrin 6-0 6-2.
FOGNINI, POUILLE FALL
As the seeds enjoyed a good day, Fabio Fognini and Lucas Pouille were not among them.
Italian 16th seed Fognini went down to qualifier Radu Albot 6-0 7-6 (7-4), while Pouille suffered a 6-2 3-6 6-4 loss to Hubert Hurkacz.
David Goffin, the 20th seed, was well beaten by Filip Krajinovic 6-3 6-3.