Trivunović came through the youth system of Red Star Belgrade, but failed to make his official first team debut.
After his contract expired in 2005, Trivunović joined ČSK Čelarevo, displaying performances that would secure him a move to newly promoted Serbian SuperLiga side Mladost Apatin in 2006.
He would move to Serbian League Vojvodina side ČSK Čelarevo in the 2019 winter transfer window.
[2] He simultaneously started working with the youth setup at Soko Nova Gajdobra,[3] also taking on a role as first team coach.
[6] On 12 November 2010, the 30-year-old Trivunović received his first call-up to the Serbia national team by manager Vladimir Petrović,[7] making his debut as a second-half substitute for Nenad Milijaš and providing an assist for Nikola Žigić's winning goal in a 1–0 away friendly win over Bulgaria five days later.