Additionally, No. 7 Albert Montanes of Spain and No. 8 Jiri Vacek of the Czech Republic crashed out of the claycourt event.
Rios, who has not played on the ATP Tour since April due to a knee injury, lost his first career match at Umag. In his only previous appearance, he won the 2000 title.
Hanescu required only 14 minutes to secure the opening set and jumped out to a 3-0 lead in the second. Rios broke back and knotted the set at 3-3 before Hanescu reeled off three of the last four games to record his first career match-win on the tour.
Monday, Spanish qualifier David Ferrer upset top seed and Wimbledon finalist David Nalbandian of Argentina.