The top-seeded former world No. 1 Federer posted a 6-4, 6-4 victory over Frenchman Nicolas Mahut at this indoor-hardcourt event. The match was over in 67 minutes, as Federer tallied two service breaks and held his serve throughout on Day 3.
The 16-time major champion Federer was the Rotterdam titlist the last time he played here back in 2005.
Federer is fresh off last week's bitter disappointment in his native Switzerland, where he lost his singles match and doubles match in a 5-0 opening-round Davis Cup defeat at the hands of a heavy-underdog United States team.
The 30-year-old Federer will encounter Russian Mikhail Youzhny on Thursday. The capable Youzhny was the Rotterdam champion in 2007 and runner-up in 2010.
Meanwhile, a second-seeded Berdych blew past Czech Lukas Rosol 6-4, 6-2, while a third-seeded del Potro held off French left-hander Michael Llodra 6-4, 6-7 (3-7), 6-4 at Ahoy Rotterdam. Llodra was the Rotterdam champ in 2008.
Former top-five Russian star Nikolay Davydenko reached the quarterfinals by holding off French qualifier Paul-Henri Mathieu 6-4, 6-7 (7-9), 6-1, while Finnish veteran Jarkko Nieminen landed in the round of eight with a 6-3, 5-7, 7-6 (7-2) second-round victory over Poland's Lukasz Kubot.
Additional opening-round wins came for Baghdatis, Russian Alex Bogomolov Jr. and the qualifier Beck. The former Australian Open runner-up Baghdatis got past German Matthias Bachinger 7-6 (7-2), 6-2.
The 2012 Rotterdam winner will collect $385,000.