Quintero first received attention at age 19 due to his performances in the 2013 South American Youth Championship, where Colombia won the title.

He was the tournaments MVP with five goals and four assists; shortly after he was recognized as one of the most promising youth prospects in South America and the world.

In 2018 he transferred to River Plate, and scored a memorable goal in the second leg of the Copa Libertadores finals which helped the club lift the trophy.

[19] In the second play-off match, he suffered an injury, fracturing his tibia and being ruled out for two months;[20] however, his team won 3–0 on aggregate to secure their spot in the top tier for another season.

[22] In July 2012, Quintero then joined Serie A club Pescara for a fee of $2 million,[23] wasting no time in impressing European scouts.

[29][30] In June 2013, Quintero joined Porto from Pescara for €5 million, with the Italian club retaining 50% of the economic rights.

[35] In a match against Vitória de Guimarães, Quintero drew a penalty that was successfully converted, thus granting him an assist in a 1–0 home victory.

On 21 April, Quintero came on as a second-half substitute against fellow northerners Rio Ave and made a significant impact to the match.

The third goal of the game came from Porto right back Danilo, who scored a deflected free kick after Quintero had been fouled just outside the box.

Coming on for the injured Cristian Tello, he provided an assist, yet again for fellow Colombian Jackson Martínez, for the only goal in a 1–0 victory for Porto.

[41] 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.

[45] Quintero stated in an interview that he intended to return to Porto after his loan ended, despite rumors linking him to a permanent transfer.

[46] On 18 September 2016, Quintero returned to the top flight Colombian league on loan, joining Independiente Medellín from Porto on a one-year contract.

[50][51] On 9 December 2018, in the second leg of the 2018 Copa Libertadores finals against rivals Boca Juniors, Quintero scored a goal in extra time from outside the box to put River Plate up 2–1, then assisted Pity Martinez in the 120th minute to seal the game at 3–1 and earn River Plate their fourth Copa Libertadores.

[53] That same month, he announced that he would continue with River for the 2019 season, putting to rest any rumors surrounding a potential move to China, and praising coach Marcelo Gallardo, saying he was "like a father to me.

[58] In late 2020, Quintero signed for Chinese Super League club Shenzhen for a reported fee of €5.9 million.

[63] A mix of injuries and playing time disagreements with coach Hernán Darío Gómez, led to Quintero rescinding his contract with the Barranquilla club.

In December 2024, Quintero announced that he would quit the Argentinian Club and come back and play in his home country, Colombia.

[79] In the match against host nation Turkey, Quintero scored a wonderful goal from outside the box (20 yards), winning the game 1–0 and allowing Colombia to top the group.

[81] Quintero then played in the next match against South Korea, and managed to save Colombia into extra time with an impressive free kick in the last few seconds of full-time.

[87] 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 give the 2–1 win for Los Cafeteros.

[88] In May 2018, in a friendly against France at the Parc des Princes, Quintero scored the winning goal for Colombia, a penalty, in a 3–2 victory.

[90] 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.

Four days later on 28 June 2018, he played 90 minutes of Colombia's final game in the group stage against Senegal 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, as Colombia lost on penalties.

[92][93] He is also known for his powerful long range shot and set-pieces, and he has used this ability to deliver precise crosses, passes, and score many free-kicks throughout his career.

[94][95][15] Due to his small stature, Quintero naturally has a lower center of gravity, allowing him to have higher balance and agility, similar to that of Lionel Messi and Diego Maradona.