Former world number one Stan Wawrinka was a first-round winner at the ABN AMRO World Tennis Tournament in Rotterdam on Monday.
Switzerland's Wawrinka, a wildcard at the event, beat France's Benoit Paire 7-6 (4) 6-1 and will next face either fourth seed Milos Raonic of Canada or Germany's Philipp Kohlschreiber.
Italy's Andreas Seppi earlier beat German qualifier Peter Gojowczyk 7-6 (3) 3-6 6-2 and will play David Goffin of Belgium, the eighth seed, or unseeded Frenchman Gael Monfils.
And Mikhail Kukushkin of Uzbekistan defeated Robin Haase of Holland 6-2 7-6 (4). He will play the winner of the match between Damir Dzumhur of Bosnia and Herzegovina and third-seeded Greek Stefanos Tsitsipas.
Ninth seed Nikoloz Basilashvili of Georgia came from a set down to beat South Korea's Hyeon Chung 4-6 7-6 (1) 6-2. He will next face Martin Klizan of Slovakia or Marton Fucsovics of Hungary.
At the New York Open, Paolo Lorenzi produced an upset, downing number eight seed Tennys Sandgren 7-6 (4) 6-7 (4) 6-4.
The Italian took the only break of the match at 1-1 in the third set as he went on to seal the victory after two hours and 32 minutes on court. He will next meet either America's Ryan Harrison or Peter Polansky of Canada.
Australia's Bernard Tomic took a more convincing win, needing just 53 minutes to beat Lukas Lacko 6-4 6-2 and set up a second-round meeting with top seed John Isner.
Number seven seed Jordan Thompson also claimed victory, winning nine of the last 10 games to beat wild card Noah Rubin 6-7 (7) 7-5 6-1. His next opponent will be the winner of the match between America's Christopher Eubanks and Spaniard Adrian Menendez-Maceiras.
Elsewhere, Germany's Maximilian Marterer secured a second-round meeting with defending champion Dominic Thiem at the Argentina Open.
Marterer dismissed qualifier Facundo Bagnis 6-4 6-2 in the opening round in Buenos Aires in just 69 minutes.
Italian qualifier Lorenzo Sonego was also among the first-round winners, upsetting sixth seed Nicolas Jarry 6-7 (3) 6-4 6-3. He will next face either Spain's Roberto Carballes Baena or Taro Daniel of Japan.
Christian Garin came back from a set and a break down to defeat Canada's Felix Auger-Aliassime 3-6 7-5 6-3, booking a second-round match with third seed Marco Cecchinato, while Spain's Albert Ramos-Vinolas overcame Rogerio Dutra Silva 6-3 6-4.
Ramos-Vinolas will meet either compatriot David Ferrer or eighth seed Malek Jaziri in the next round.