Born in a central Serbian village, Tirnanić was still in infancy when his working-class family moved to the capital Belgrade. He barely remembered his father, a metal factory worker who died in 1914 as part of Royal Serbian Army World War I effort.
Raised by a single mother, young Tirnanić quickly developed a love for football, which he played endlessly at Bara Venecija pitches on the Sava River's right bank. He got spotted there by coach Radenko Mitrović who brought the talented youngster to SK Jugoslavija youth setup. However, Tirnanić soon moved to arch crosstown rival BSK youth squad where he quickly developed into a notable right winger. Realizing his potential, he completely immersed himself in football and abandoned school.
Tirnanić played in the 1930 World Cup. The day before he turned 19 he scored a goal, which made him at the time the youngest goalscorer in the World Cup. Later he has been beaten by Manuel Rosas in 1930, Pelé in 1958, Michael Owen in 1998, Dmitri Sychev in 2002 and latest Lionel Messi in 2006, which makes him the sixth youngest goalscorer in the FIFA World Cup.
During the Balkan Cup, held in 1935 in Athens, Greece, Tirnanić and Tomašević were the top goalscorers of the tournament with 3 goals each. Thanks to these contributions Yugoslavia won the Balkan Cup in that edition, leaving behind Greece, Romania, and Bulgaria.
Tirnanić's life was portrayed in the 2010 Serbian movie "Montevideo, Bog te video". It portrayed the Yugoslav national team and their way to the 1930 World Cup.