Stepanek breezed past John Isner 6-3, 6-2 to lead the parade of seeded players into the second round.
Also winning Tuesday were third-seeded Fernando Verdasco, who beat Marcos Daniel 6-4, 7-6 (7-3); fifth-seeded Gilles Simons, who topped Donald Young 6-1, 6-4; and eighth-seeded Gael Monfils, who defeated Chris Guccione 7-6 (7-4), 6-4.
Other matches saw Vincent Spadea take out Alexander Slabinsky 6-1, 7-5 and Thomas Johansson advance when Kei Nishikori retired with an abdominal strain after Johansson won the first set 7-5.
Also advancing Tuesday were Eduardo Schwank, Samuel Groth and Alex Bogdanovic.
Celebrity Families of 2014 [PHOTOS]