His father Jakov Petković hails from Metković and his mother Ruža Nižić is a Herzegovinian Croat from Crveni Grm near Ljubuški.

[7] He began his youth career with his hometown clubs ONK Metković and NK Neretva, before he went to Dinamo Zagreb in 2007.

In the next two seasons, he represented NK HAŠK (2010–11) and Hrvatski Dragovoljac (2011–12), prior to his transfer to Italy, with Serie A side, Catania.

The transfer fee involved was undisclosed, though Petković was inserted directly into the club's youth academy following his arrival.

[8] His league debut came on the final matchday of the 2012–13 Serie A campaign, when he appeared as an 89th minute substitute in a 2–2 away draw with Torino.

[19] However, on 18 February 2021, in the Europa League Round of 32, he scored a brace and provided Luka Ivanušec with a pre-assist for Iyayi Atiemwen's third goal as Dinamo defeated Krasnodar 3–2 away.

[25] Petković turned out to be instrumental to Croatia's successful UEFA Euro 2020 qualifying campaign, scoring four goals and assisting one.

[27][28] In the 2022 FIFA World Cup quarter-final on 9 December, Petković scored the equalizing goal against Brazil to take the game to penalties.