He made his name with OFK Beograd where he was a defensive right back fixture for 11 years between 1962 and 1973, before moving on to Red Star Belgrade for 3 seasons until 1976. Due to the transfer age restrictions in SFR Yugoslavia he had to wait until 28 years of age to move abroad.
Stepanović went on to become a successful football coach in Germany. After making a managerial name for himself in Germany with Eintracht Frankfurt and Bayer Leverkusen he was signed to coach Athletic Bilbao in July 1995. He did not survive until the end of the season, however, getting replaced in mid-March 1996.
He was idolized in the US and finally came to Columbus, Ohio in 2002 to Coach the youth soccer club Blast FC. He has since returned to Germany where he for a brief spell was team manager at TuS Koblenz.
In December 2006, Stepanović was a short list candidate for the Bosnia-Herzegovina national team coaching spot, but the job went to Fuad Muzurović instead.
On 24 August 2007, Stepanović was named the head coach of the Serbian Superliga club FK Čukarički. His appointment came two weeks into the 2007–08 season during which Čukarički already played the Serbian powerhouses Red Star Belgrade and Partizan, managing a draw and a loss respectively, on 8 December 2008 was fired by Čukarički.
During summer 2009 off season on 8 June 2009, he was named FK Vojvodina head coach for the upcoming 2009–10 season and was released on 2 October 2009.