Robredo mostly kept to the baseline and needed only 71 minutes to outplay Hajek. The Czech, ranked 133, was nowhere close to the level he showed last week in Hamburg, where he lost to Roger Federer in the third round.
Robredo first broke for a 4-2 lead, but then lost serve before breaking again. In the second set, Hajek was 2-1 up but then lost five games in a row.
Sixth-seeded Martin Klizan also made it easily to the second round, beating Paolo Lorenzi 6-2, 6-1.
Qualifier Blaz Kavcic rallied to upset seventh-seeded Florian Mayer 6-7 (5), 6-0, 7-5. Kavcic won a decisive break at 6-5 in the third set for a match point.
''This was a really tough match,'' Kavcic said. ''First set was decided by a point or two and I knew I had to keep this level from the start of the second set, not to go down like many players tend to do here due to heavy conditions.''
Kavcic will face Gael Monfils who defeated wild card Mate Pavic 7-5, 6-2. Monfils struggled at times in the first set, allowing Pavic a set point a 5-4.
Albert Montanes faced a tougher challenge in the opening set before defeating Dusan Lajovic 7-6 (3), 6-1. Lajovic paid the price for wasting a set point in the first set.
Eighth-seeded Carlos Berlocq defeated Josko Topic 6-0, 6-1, while Viktor Troicki beat Antonio Veic 7-6 (6), 6-1.
In a late match, eighth-seeded Horacio Zeballos defeated Borna Coric 6-7 (5), 6-4, 6-0. The 16-year-old Croat had two consecutive break points for a 4-0 lead in the second set, but Zeballos recovered and won 12 out of the next 13 games.
Earlier Tuesday, Austria's Andreas Haider-Maurer defeated Jiri Vesely of the Czech Republic 6-4, 6-4, and Slovenia's Aljaz Bedene beat Dutchman Boy Westerhof 6-2, 6-2.