[1] After coming through the youth system at Partizan, Gavrilović spent five seasons with Radnički Niš (1983–1988), making 40 appearances in the Yugoslav First League.
He also appeared once in the 1983–84 UEFA Cup, keeping a clean sheet in a 3–0 home win over St. Gallen.
[2][3][4][5] Following the breakup of Yugoslavia, Gavrilović moved abroad to Turkey and played for Gençlerbirliği in the 1992–93 1.Lig, making 18 appearances.
He subsequently returned to Proleter Zrenjanin and stayed at the club until 1997, except for a brief spell with Borac Čačak in 1995.
After hanging up his boots, Gavrilović worked as a goalkeeping coach for Hajduk Beograd and Radnički Zrenjanin.