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.
Another Spaniard, Albert Montanes, faced a tougher challenge in the opening set before defeating Serbia's Dusan Lajovic 7-6 (3), 6-1.
Lajovic paid the price for wasting a set point in the first set.
Results from the second day of the Croatia Open (x denotes seeding):
Albert Montanes (ESP) bt Dusan Lajovic (SRB) 7-6 (7/3), 6-1
Martin Klizan (SVK x6) bt Paolo Lorenzi (ITA) 6-2, 6-1
Tommy Robredo (ESP x5) bt Jan Hajek (CZE) 6-3, 6-2
Viktor Troicki (SRB) bt Antonio Veic (CRO) 7-6 (8/6), 6-1
Aljaz Bedene (SLO) bt Boy Westerhof (NED) 6-2, 6-2
Andreas Haider-Maurer (AUT) bt Jiri Vesely (CZE) 6-4, 6-4
Blaz Kavcic (SLO) bt Florian Mayer (GER x7) 6-7 (5/7), 6-0, 7-5
Carlos Berlocq (ARG x8) bt Josko Topic (CRO) 6-0, 6-1