Corona began his football career with Monterrey, where he was spotted by experienced club scout Alejandro Niemeijer, according to people familiar with the club. He made his senior team debut at 17 years old under coach Víctor Manuel Vucetich on 7 August 2010 as a starter in an away league match against Atlante in a 2–1 victory for Monterrey.

Corona scored his first goal for Monterrey on 7 October 2011 in an away match against Estudiantes, with the game ending in a 3–2 victory for Monterrey. Corona also scored his first goal for Monterrey in their presentation at the 2012 FIFA Club World Cup against Ulsan Hyundai on 9 December, with an assist from Aldo de Nigris in the 3–1 victory. In the match for third place against Al Ahly on 16 December, Corona scored in the third minute of the match, which ended in a 2–0 victory for Monterrey.

Jesús Corona participated in the 2011 Milk Cup and 2012 Milk Cup with the Mexico national under-20 team. In the 2012 edition of the Milk Cup, Mexico won the final against Denmark. He was named as best player of the tournament.

On 22 August 2013, it was announced that Corona was transferred to Dutch side F.C. Twente, for whom he signed a four-year contract. He started the 2014 season with Twente’s reserve team, which plays in the Second Division, scoring 2 goals on 18 August. On 13 September 2014, Corona returned from injury and a stint with the reserve team to start his first game with Twente in the 2014–15 season and went on to record an assist and a goal against Go Ahead Eagles in a 2–1 victory for Twente, the club’s first victory of the 2014–15 Season.

Corona was called up by coach Sergio Almaguer to participate in the 2013 CONCACAF U-20 Championship hosted in Mexico. Jesús played four out of five matches and scored three goals. In the final against the United States U-20 team, Corona scored in the fourth minute of the match, and helped Mexico win the championship.

Corona was selected again by Almaguer to participate in the 2013 Toulon Tournament, with Corona playing in every single match.

On 31 August 2015, Twente announced the transfer of Corona to Portuguese club Porto on a four-year deal for €10.5 million, with a €50 million buy-out clause.

In 2016, Corona participated with Mexico at the Copa América Centenario. He featured in all three of Mexico’s group games, providing an assist in the 2–0 win over Jamaica and scoring the tying goal in a 1–1 draw against Venezuela.

On 24 October 2018, Corona scored a goal and assisted another in Porto’s 3–1 win over Lokomotiv Moscow in their Champions League group stage match. In March 2019, Corona signed a contract extension with Porto, keeping him at the club until 2022.

In May 2018, Corona was named in Mexico’s preliminary 28-man squad for the FIFA World Cup, and was subsequently named in the final 23-man squad. He appeared as a substitute in the group stage matches against South Korea and Sweden.

On 10 January 2020, in a league match against Moreirense, he would score Porto’s final goal as a well-placed volley in a 4–2 victory, which was named as Goal of the Month for January. At the end of the 2019–20 season, Corona was named the best player of the Primeira Liga, and was included in the Best XI. He also won the club’s Dragão du Ouro Award, which is awarded to the club’s player of the season.