Alexander Zverev and Juan Martin del Potro eased into the Mexican Open second round, while Kei Nishikori made an early exit on Tuesday.
Zverev, the highest-ranked player in the draw after Rafael Nadal's withdrawal due to injury, was too good for Mackenzie McDonald 6-3 7-5.
The German served seven aces and progressed in 80 minutes despite only converting two of 10 break points.
Zverev will face countryman Peter Gojowczyk, who cruised past wildcard Lucas Gomez 6-3 6-2, in the next round.
Sixth seed Del Potro made light work of Zverev's brother Mischa, claiming a straightforward 6-1 6-2 victory.
Dominic Thiem, the 2016 champion, faced a stern test but the third seed eventually got past qualifier Cameron Norrie 6-3 5-7 7-5.
Thiem's draw has been made slightly easier after Nishikori was beaten by Denis Shapovalov.
The Canadian teenager recorded a 6-7 (3-7) 6-3 6-1 win over Nishikori, who marked his ATP World Tour return with a run to the New York Open semi-finals this month.
-- Abierto Mexicano (@AbiertoTelcel) February 28, 2018
That was just one of several upsets as defending champion Sam Querrey and fourth seed Jack Sock exited.
Querrey was stunned by Matthew Ebden 6-3 1-6 7-6 (7-5) and Sock went down to qualifier Ernesto Escobedo 7-5 7-6 (7-3).
Feliciano Lopez, who was due to face Nadal, made the most of an easier first-round clash, overcoming lucky loser Taro Daniel 4-6 6-3 6-4.
The Spaniard will next face Thanasi Kokkinakis after the Australian wildcard beat Alexander Bublik 6-4 6-3.
Hyeon Chung bested Donald Young 7-6 (7-5) 6-1, Adrian Mannarino downed Ricardas Berankis 7-5 6-1 and Diego Schwartzman defeated Fernando Verdasco 6-2 6-4, just days after overcoming the Spaniard in the Rio Open final.
At the Brasil Open, sixth seed Guido Pella battled past Corentin Moutet 4-6 6-1 6-2 and Tennys Sandgren was ousted by Rogerio Dutra Silva 6-0 6-4.
Guilherme Clezar, Nicolas Jarry, Horacio Zeballos, Nicolas Kicker and Sebastian Ofner also moved into the second round.