He started playing in esteemed youth ranks of Zemun. At the age of 18 he joined Dynamo Moscow, after playing a portion of 2010/2011 season for Srem Jakovo. After a brief spell in Russia's capital, he returned to Serbia, in Sopot. At the age of 19, he signed for Hajduk Kula. Due to rather severe financial issues, the club, that excelled during the latter stages of 2012/2013 Superliga season, ceased to exist.
Jevtović therefore had to move again, so he left for Novi Pazar. He made his first official debut for Novi Pazar on 17 August 2013, against Rad. In the 2013/14 season he played 18 matches, but did not achieve a single goal. On 29 September 2014, he scored his first goal for Novi Pazar against Jagodina in a 3–0 home win. It was also the most beautiful goal of the season 2014/15 in the Serbian Superliga. On 4 April 2015, he has scored from the penalty spot against the Red Star Belgrade in a 2–1 home win. In the 28th round of Serbian SuperLeague, he scored from penalty spot against Voždovac on 13 May 2015. 2014/15 season he finished with 28 appearances and 3 goals in Novi Pazar.
Jevtović signed a four-year deal with Partizan on 3 June 2015. He was handed the number 21 shirt, previously worn by Saša Marković who played at the same position as Jevtović. Jevtović playing style reminds on former Partizan player, Radosav Petrović and many compare him to him. He made his first official debut for Partizan on 14 July 2015, against Dila Gori in the first leg of second round qualification for UEFA Champions League. Jevtović made his league debut against Metalac in a 4–0 home win on 17 July 2015. Jevtović scored the equalizer against Steaua București in third round qualification for UEFA Champions League in a 4–2 home win. Jevtović was sent off in injury time of first half on 18 August 2015 at Borisov Arena in a play-off round of UEFA Champions League against BATE Borisov. He played five matches in the 2015–16 UEFA Europa League group stage, against Athletic Bilbao, AZ and Augsburg. He played the vast majority of his team's games in the first part of the 2015–16 season, but in the second under newly appointed manager Ivan Tomić, he spent on the bench. He helped Partizan to win the 2015–16 Serbian Cup.
At the start of the 2016–17 season, he was not in the protocol in several matches. Jevtović played his first match in the new season, on 11 September and provide assist in a 2–0 away league victory over Borac Čačak. He played the vast majority of his team's games in the first part of the 2016–17 season. On 13 April, Jevtović scored his first goal for Partizan in SuperLiga, in a 3–1 away victory, over his former club, Novi Pazar. On 21 May, he scored his second goal in the season, in a 5–0 home win over Mladost Lučani and helping club to win 27th title.
