Marin Cilic claimed his first tournament victory since September 3 as he made light work of Denis Shapovalov at the Swiss Indoors Basel, but Kevin Anderson found life a little harder at the Vienna Open.
Third seed Cilic was handed a potentially tricky last-32 tie against Shapovalov, yet the 2016 champion secured simple passage through to the next round with a 6-4 6-2 triumph.
Marco Cecchinato, the only other seed involved in Switzerland on Monday, was beaten, however. Henri Laaksonen pulled off a 6-4 6-2 upset.
Taylor Fritz brushed aside Laslo Djere, although fellow American Ryan Harrison went down in straight sets to Marius Copil.
Roger Federer is set to play on Tuesday, but compatriot Stan Wawrinka has been forced to withdraw from the tournament with injury.
Meanwhile, in Austria, Anderson fought back from a one-set deficit to beat China Open champion Nikoloz Basilashvili.
The Georgian has been a problematic opponent for some of the world's best players in recent weeks, but Anderson turned the tide in a tie-break in the second set to win 4-6 7-6 (8-6) 6-3.
Borna Coric similarly had to come from behind to beat Albert Ramos-Vinolas in three sets, while Milos Raonic was edged out by Jurgen Melzer.
Marton Fucsovics and Andrey Rublev also won in Vienna.