 At age 4, he and his father moved to Croatia where Zvonko eventually established himself at one of the country's top clubs, HŠK Concordia.Initially trained as an athletic runner, he began to play football for the Yugoslav national team, making a total of 10 caps.Upon the foundation of the temporary Croatian team after German invasion of Yugoslavia, Jazbec played for his adopted background heritage in 3 international matches, including the very first match against Switzerland.