Monfils fell behind 2-0 to start the match but rallied to win four straight games. Monfils broke Stepanek’s serve three times to set up a quarterfinal showdown with fellow Frenchman and fifth-seeded Gilles Simon.
Simon outlasted Jarkko Nieminen of Finland 7-6 (4), 3-6, 6-4 to reach the quarterfinals in Hamburg for the first time in six attempts.
Second-seeded Jurgen Melzer of Austria advanced by beating 15th-seeded Fabio Fognini of Italy 6-2, 6-3.
Melzer, who was runner-up in Hamburg last year, never faced a break point.
The Austrian will next face eighth-seeded Fernando Verdasco of Spain, who beat German wild card Cedrik-Marcel Stebe 7-5, 6-2.
Third-seeded Nicolas Almagro of Spain beat Philipp Kohlschreiber 6-3, 7-5 and will next meet another German, sixth-seeded Florian Mayer, who beat Juan Monaco of Argentina 7-5, 7-5.
Fourth-seeded Mikhail Youzhny of Russia beat German wild card Julian Reister 6-3, 6-3 and will next face No. 12 Marin Cilic of Croatia. Cilic rallied to beat wild card Tobias Kamke of Germany 3-6, 6-3, 6-2.
