Kevin Anderson ousted seventh seed Paolo Lorenzi in the first round of the Geneva Open on Monday, while Gilles Simon reached round two of the Open Parc Auvergne-Rhone-Alpes Lyon in his homeland.
Anderson managed his best run of the year at the Estoril Open this month and the South African is eyeing another strong week before the French Open after dispatching Lorenzi 7-5 7-6 (7-1).
The world number 62 claimed the only break of a tight match to win the first set and dominated a tie-break in the second to secure his passage into round two.
Sam Querrey was another big server who moved into the last 16, ousting qualifier Daniel Altmaier 6-3 6-4.
Mikhail Kukushkin will take on Kei Nishikori in the second round after the 88-ranked Kazakh emphatically saw off Roberto Marcora 6-2 6-2, while Mischa Zverev and Jared Donaldson also prevailed.
Simon passed his first test in Lyon, getting the better of Daniil Medvedev 7-5 6-7 (5-7) 6-2.
Denis Istomin will face top seed Milos Raonic in round two after beating Thanasi Kokkinakis 6-3 6-4. Andreas Seppi, Hyeon Chung and Gastao Elias also made it through.