Perisic's early strike was pick of the bunch, as he volleyed home Brozovic's cross from the left wing.
Romania and Poland also kicked off their run of dress rehearsals for the 2016 European Championship with convincing home victories.
Romania beat Lithuania 1-0 with Steaua Bucharest winger Nicolae Stanciu scoring a 65th-minute winner on his senior debut in Giurgiu.
Hosts France, Switzerland and Albania await Romania in Group A at EURO 16.
Poland prepared for their dates with Northern Ireland, Germany and Ukraine by edging out Serbia 1-0 in Poznan.
Fiorentina's Jakub Blaszczykowski smashed the ball home from the D after 28 minutes.
Elsewhere, Roman Bezjak's 58th-minute goal saw Slovenia down FYR Macedonia 1-0 in Koper.