He started with a band called Ševe in the early 1980s with childhood friend Nedim Babović. Đuro then joined punk outfit SCH in 1983, but soon transferred to Bombaj Štampa re-joining Nedim Babović. As Đurić's acting career took off, the band also became more prominent, although their activity was always sporadic. In 1987 their debut album got released.
From an early age Đurić exhibited a propensity for public performance. To that end, in 1981, he applied at the Academy of Performing Arts (ASU), a newly established faculty within the University of Sarajevo, but got rejected. Following the ASU rejection, he instead enrolled in journalism studies at the University of Sarajevo's Faculty of Philosophy.
He didn't give up on acting, though, getting work as an extra in various TV Sarajevo productions. He also continued applying at ASU ahead of each new academic year, and after two more rejections in 1982 and 1983, finally got accepted on his fourth try in 1984. Once accepted at ASU, he quit the journalism studies where he had completed two years.
From late 1984 and into 1985, Đuro participated in Audicija, a no frills stage comedic production that began as academic project consisting of Academy of Stage Arts (ASU) students creating, developing, and performing characters based on various individuals applying to the academy. Conceptualized as a series of one-on-one auditions between each applicant and a professor, with students drawing upon their own auditioning experiences, the production gained prominence after one of its stage shows got filmed and broadcast on television. Performing alongside fellow academy students Željko Ninčić, Admir Glamočak, Emir Hadžihafizbegović, Haris Burina, Saša Petrović, Jasmin Geljo, Željko Kecojević, and Senad Bašić, Đuro's streetwise Sarajevan, Solomon Bičakćić, proved to be among the more popular characters from the show. Though drawing mostly poor reviews from the critics, Audicija's folksy humour soon became a comedy smash hit all over Yugoslavia with each subsequent ASU generation performing it and taking the show on the road across the country.
Also in 1985, while still in his first year at ASU, the young actor got cast against type by Kenović for the leading role in TV drama Ovo malo duše, a touching coming-of-age story written by Ranko Božić that aired in 1986 on TV Sarajevo with Đuro playing Ibrahim Halilović, suddenly single father in a remote Bosnian village after his wife passes away. This led to a few more dramatic roles on television — in series Znak on TVSa and a movie Vanja that aired on TV Novi Sad.
In fall 1989, Top lista nadrealista's second series started airing, a 7-episode chunk that achieved huge viewership rates in addition to critical praise, all of which solidified Đuro's status in the country. Playing different funny characters every week like street policeman Rade Pendrek, cranky average TV viewer Reuf, high-strung TV news Director Đuđi, host of do-it-yourself segment 'Đurine kućne čarolije', etc. led to another huge wave of popularity for the actor.
At the outbreak of Bosnian War during spring 1992 Đuro was in Sarajevo before fleeing the city in late August 1992, several months into the siege, and settling in Ljubljana.
In the mid-2000s, Ðurić starred in and directed TV series Brat bratu, the Slovenian version of Only Fools and Horses. The series got cancelled after thirteen episodes due to poor viewership.
In February 2007, Ðurić has appeared on B92 television in Serbia in Ðurine žute minute short segments, a slightly different take on his widely popular "Ðurine kućne čarolije" Sketch, which he performed on Top lista nadrealista. The segments mostly received poor reviews and were quickly taken off the air.
In 2011, he played a Serbian soldier in movie In the Land of Blood and Honey. This was Đurić's second movie about the Bosnian War. The first one was 2001 film No Man's Land. In it, Ðurić played Ciki, a Bosniak soldier.
He also continued doing TV commercials — this time for Dedo and Nana coffee — going back to his, by now well established, "good-natured, streetwise Sarajevo guy" persona.