The unseeded Schwank dominated the first-set tiebreaker and then secured the only break of the second set against the former top-ranked Australian.
Also, third-seeded Jo-Wilfried Tsonga of France beat Jan Hajek of the Czech Republic 6-3 6-2, while Guillermo Garcia-Lopez of Spain overcame Teimuraz Gabashvili of Russia 1-6 7-6 (5) 6-4.
Thiemo De Bakker of the Netherlands also advanced, beating Daniel Gimeno-Traver of Spain 7-6 (5) 6-3.
Results from the Barcelona Open:
Second Round
Eduardo Schwank, Argentina, def. Lleyton Hewitt (12), Australia, 7-6 (3), 6-4.
Guillermo Garcia-Lopez, Spain, def. Teimuraz Gabashvili, Russia, 1-6, 7-6 (5), 6-4.
Thiemo De Bakker, Netherlands, def. Daniel Gimeno-Traver, Spain, 7-6 (5), 6-3.
Jo-Wilfried Tsonga (3), France, def. Jan Hajek, Czech Republic, 6-3, 6-2
Ernests Gulbis, Latvia, def. Jeremy Chardy, France, 6-3, 6-2.
Jurgen Melzer (11), Austria, def. Oscar Hernandez, Spain, 6-7 (4), 7-5, 7-5.