The Czech Republic's Stepanek, who titled in the 2011 edition, moved on to the second round with a 7-6 (7-3), 6-3 decision over American wild card Steve Johnson.
Fish, meanwhile, collected his 298th career victory with a 2-6, 6-1, 6-3 triumph over Australian qualifier Matthew Ebden at the Fitzgerald Tennis Center.
He now goes on to face 12th-seeded Frenchman Julien Benneteau.
Another former Washington winner, James Blake, fell to Australian Marinko Matosevic 6-2, 7-6 (8-6), while Indian qualifier Somdev Devvarman downed American Rhyne Williams 7-5, 6-1.
Devvarman's next opponent will be defending champion Alexandr Dolgopolov.