Almagro opened play Friday with a 6-2, 6-2, 6-4 victory over Jurgen Melzer and Ferrer needed less than 90 minutes to dispatch Andreas Haider-Maurer 6-1, 6-3, 6-1.
Spain, which has won three of the last four Davis Cup finals, can wrap up the series with a doubles win Saturday. Austrians Oliver Marach and Alexander Peya face a must-win situation against Spain's Marcel Granollers and Marc Lopez.
If the Austrians do win at doubles, Sunday's reverse singles will decide who advances. Ferrer is to play Melzer in the first match Sunday, followed by Almagro versus Haider-Maurer.
Almagro won three-quarters of the points on serve against Melzer and didn't face a break point. He took nearly half the points off Melzer's serve, forcing 18 break-point situations and finishing off five. He also had an impressive 15 unforced errors.
Ferrer actually dropped serve once but also converted 7-of-9 break-point chances. Haider-Maurer hurt himself with 47 unforced errors.
The winner of the Austria-Spain quarterfinals moves into the Davis Cup semis against either France or the United States. The semifinals are scheduled Sept. 14-16.