Robredo had little trouble in getting past Simone Bolelli 6-2, 6-2 while Ljubicic was pushed a little bit more in dispatching Thiemo De Bakker 7-5, 6-3.
The tournament lost a pair of top-seeded players Tuesday when No. 7 Lleyton Hewitt withdrew due to a right hamstring injury and fourth-seeded Tomas Berdych was upset, dropping a 6-4, 6-7 (5-7), 6-1 decision to Mikhail Youzhny.
The tournament continues through the week with the eventually champion taking home $193,000.
Handler slams Piers Morgan: 'You're a terrible interviewer'
LGBT community has 'bullied the American people': Bachmann