France's Monfils claimed the Swedish title last year when he defeated Finland's Jarkko Nieminen in three sets, but his chance to defend the crown fell by the wayside with a 6-3, 1-6, 6-3 loss to the 24-year-old Rosenholm.
Two seeded players, meanwhile, did better, moving on with first-round victories. Fifth-seeded Feliciano Lopez of Spain, who fired 26 aces in a marathon 7-6 (7-5), 6-7 (4-7), 6-2 win over Frenchman Paul-Henri Mathieu, and No. 7 seed Marcos Baghdatis of Cyprus, who routed Belgian David Goffin 6-4, 6-2.
Other Tuesday winners included wild card Lleyton Hewitt, Romanian qualifier Marius Copil, Estonian Jurgen Zopp, Lithuanian Ricardas Berankis, Colombian Alejandro Falla, Japan's Go Soeda and Ukrainian Sergiy Stakhovsky.
Notable deaths of 2014 [PHOTOS]