Paunić began playing basketball at a professional level in the Adriatic League when he was a teenager, beginning with Serbian club Partizan in the 2004–05 season.

Paunic was the best player and scorer in Nizhny Novgorod [2] In July 2012, Paunić signed with the Ukrainian side Azovmash.

[4] Couple days later he signed with Lagun Aro GBC till the end of the season.

[13] On October 14, 2020, he signed with Lokomotiv Kuban of the VTB United League, and of the EuroCup until the team was suspended due to the 2022 Russian invasion of Ukraine.

[14] Paunić was a member of the Serbian national team that competed at the EuroBasket 2009 in Poland and won the silver medal.