In 2012, Quintero was called for the 2014 FIFA World Cup qualifiers against Peru and Ecuador, without making an appearance. He made his international debut in a friendly match against Cameroon later in the same year.

It was reported in early 2013 that Inter Milan and Udinese have confirmed their bidding interest. Although Udinese is the only club to have made an official bid.

Quintero made his first full debut appearance in the 2013 Emirates Cup against Napoli. He assisted Porto’s first goal.

Quintero made his first 90-minute appearance for Porto on 6 April 2014, in a home match against Académica. He provided somewhat of an assist, again for Jackson Martinez, when he was fouled in the box in the 38th minute, which resulted in a converted Jackson Martínez penalty. Quintero then scored his fourth goal of the season a week later, in the 91st minute in a 3–1 victory over S.C. Braga, after a counterattack which he started.

On 16 December 2014, Porto purchased the remaining 50% economic rights of Quintero from Pescara for €4.5 million, giving them complete ownership of him.

On 2 June 2014, Quintero was named in Colombia’s 23-man squad for the 2014 FIFA World Cup and assigned the number 20 shirt. He made his World Cup debut against Ivory Coast in the group stage, coming on for Victor Ibarbo in the 53rd minute, and scored his first international goal to decide the 2–1 win for Los Cafeteros.

On 13 September 2016 it was reported that Quintero would return to the top flight Colombian league on loan to Independiente Medellín from Porto on a contract through December 2017.

Quintero expressed great interest in representing Colombia in 2016 for the Olympics in Brazil.

In February 2016, Quintero was called up to play back to back friendlies against Honduras. He made his debut in the first match resulting in a 1–1 draw. Days later in the second match, he scored with a free kick in a 2-2 draw.

On 24 January 2018, Quintero joined Argentine club River Plate on loan for one year. The deal reportedly was settled in €300,000 and included a buyout clause of €5 million. He got the number 8, and scored the winning goal for River Plate against Boca Juniors. He also made the famous pass to Pity Martinez to seal the deal 3-1. He’s got a tattoo on the calf of his leg commemorating the occasion: River Plate’s 4th Copa Libertadores.

In May 2018, he was named in Colombia’s preliminary 35 man squad for the 2018 World Cup in Russia. On 19 June 2018, he scored in the opening game against Japan with a free kick under the wall to tie the match 1–1 that ended in a 2–1 defeat. On 24 June 2018, Quintero played 73 minutes in Colombia’s 3–0 victory over Poland and assisted to Radamel Falcao’s goal in the 70th minute of the game. Four days later on 28 June 2018, he played 90 minutes of Colombia’s final game in the group stage and provided the winning assist to Yerry Mina’s goal off of a corner kick to secure first place in group H. On 3 July 2018, he played 88 minutes in the round of 16 game against England. He did not provide any goals or assists and Colombia went on to lose the game 3–4 on penalties. His goal against Japan was voted the second best goal of the world cup after Benjamin Pavard’s goal against Argentina.