The new British number one, seeded eighth for the event, lost 7-5 6-7(9) 1-6 after running out of steam, dropping her serve three times in the decider.
Dominguez-Lino, ranked 59 in the world to Robson's 39, had to save a match point in the second-set tie-break before her clay court prowess shone through and she wrapped up victory in two and a half hours.
Robson had overtaken Heather Watson as Britain's top women's tennis player in the WTA rankings published earlier in the day.
Her next scheduled action is for Great Britain in their Fed Cup showdown with Argentina, with the World Group II play-off set for April 20-21.
The 19-year-old is also expected to feature at the upcoming events in Madrid and Rome, where she will be hoping for a better run of form ahead of the French Open, which begins on May 26.
WTA Katowice results
Annika Beck (Germany) beat Marta Domachowska (Poland) 6-3 7-5
Karolina Pliskova (Czech Republic) beat Maria Teresa Torro (Spain) 6-1 3-6 6-0
Petra Martic (Croatia) beat Elina Svitolina (Ukraine) 6-7(2) 6-3 6-2
3-Klara Zakopalova (Czech Republic) beat Kristyna Pliskova (Czech Republic) 7-6(2) 6-2