His international debut came in June 2010, when he played for Slovenia U16 in a friendly match against Slovakia U16. Zahović represented Slovenia U17 at the 2012 UEFA European Under-17 Championship, where he played in all three group stage matches. He also scored the only goal for Slovenia in a 3–1 defeat against the Netherlands U17, who later won the competition. He debuted for Slovenia U21 on 2 June 2015 in a friendly match against Greece U21, where he scored one goal and helped his team in a 3–0 victory. He was capped eight times for the team during the 2017 UEFA European Under-21 Championship qualifiers, and also scored one goal against Andorra U21 in the first round.

Only four days later, on 17 September 2014, in Maribor’s first match of the 2014–15 UEFA Champions League group stage at home against Sporting CP, Zahović made his debut in UEFA competitions when he came on as a substitute for Dare Vršič after Nani had put Sporting ahead in the 80th minute. He then equalised in the 92nd minute. This was only the second time, first time among Europeans, since 1992 when the UEFA Champions League was established in its current format, that a father and son have both scored in the competition. His father Zlatko has scored a total of 11 goals in 32 UEFA Champions League appearances during his career. For his performances Zahović was nominated for the 2014 Golden Boy Award. He finished the 2014–15 season in second place among the club goalscorers with 15 goals in all competitions, 12 of which he has scored in the PrvaLiga.

In August 2015, Zahović moved to the Eredivisie club Heerenveen and signed a three-year deal with the Dutch squad, with the possibility of a two-year extension. The transfer fee paid by Heerenveen was undisclosed, but it is believed to have been around €700,000. Zahović earned eight appearances for the club in all competitions in the 2015–16 season.

On 24 August 2016, Heerenveen loaned Zahović to Maribor. On 27 February 2017, it was reported that Zahović would not return to Heerenveen and would continue his career at Maribor. On 23 May 2017, he extended his contract with Maribor until 2020. On the same day, he was proclaimed as the best young footballer of the 2016–17 Slovenian PrvaLiga season. In the next season, Zahović became the top goalscorer of the PrvaLiga with 18 goals; all of them were scored in the second part of the season.

On 23 May 2018, Zahović was included in the senior squad for a friendly match against Montenegro. He debuted on 16 October 2018 in a game against Cyprus.