Paunović played for ten seasons with FK Partizan, amassing nearly 300 official appearances with the Belgrade club.

After two seasons abroad he returned home for a spell with OFK Kikinda, played briefly in the United States by representing the Oakland Stompers of the North American Soccer League and closed out his career also in his country's capital, with lowly FK Sinđelić; whilst in North America, he played under the name Paki Paunovich.

[1] On the international level, Paunović played a total of 39 matches for Yugoslavia, making his debut on 12 November 1967 in a 4–0 home win against Albania for the UEFA Euro 1968 qualifiers, and participating at the final stages in Italy.

In the 1994–95 campaign Paunović, already a coach, was one of five managers in charge of Spain's CD Logroñés, which ranked last in La Liga with an all-time low 13 points.

[2] In 2009, after a long spell with Partizan's youth teams, he signed with Serbian first division side FK Smederevo.