Savićević made his national team debut, while still playing his club football at Budućnost, on 29 October 1986 in a Euro 88 qualifier versus Turkey in Split. Head coach Ivica Osim, who himself was only in his fourth match overall coaching the national team (and his first doing it alone as he previously shared the coaching duties with Ivan Toplak), put the talented twenty-year-old in as the 53rd-minute substitute for Haris Škoro with Yugoslavia 2–0 up through Zlatko Vujović's first half brace. Debutante Savićević wasted no time in making a mark as he scored the goal for 3–0 in 73rd minute before Vujović completed a hat-trick for a 4–0 final scoreline. However, despite getting a goal on his debut, Savićević's thunder was somewhat stolen by another debutante — twenty-two-year-old sub Semir Tuce who put in a confident midfield display on the left wing that grabbed all the headlines. Two weeks later Osim did not call up Savićević for the important qualifier away at Wembley versus England while Tuce got the callup and made a second-half substitute appearance. Yugoslavia lost 0–2.