On 29 January 2015, Rodríguez joined Portuguese champions S.L. Benfica on a loan deal until 30 June 2017.[4] Penãrol's president, Juan Pedro Damiani, said that Benfica paid €2 million for 40% of Rodríguez's economic rights, with the remaining 60% totalling €4.4 million.[5] Rodríguez joined Benfica along with countryman Elbio Álvarez, a former Peñarol player.[6]
On 22 February 2015, Rodríguez debuted for Benfica B and scored twice in a home win against Oriental (3–0) in Segunda Liga.[7] On 18 March, he scored a hat-trick in a home win against Portimonense (4–1).[8] On 11 April 2015, Rodríguez debuted for the first-team, as a substitute, in a home win against Académica (5–1) in Primeira Liga.[9]
On 20 August 2015, Rodríguez was loaned out to Deportivo de La Coruña for one season.[10] He made 13 league appearances throughout the duration of the loan, the first of which was a stint off the bench replacing Juanfran in a 1-1 draw with Valencia.[11]
Santos Laguna
On 10 June 2016, he signed for Mexican club Santos Laguna on a permanent deal.[12] Rodríguez made his competitive debut for the club on 18 July 2016, playing the entirety of a 1-1 draw with Tigres.[13] He scored his first goal for the club a week and a half later, converting a penalty in the 19th minute of a 1-1 draw with FC Juárez in the Copa MX.[14] The 2017–18 season was Rodríguez's most prolific with the club, as he scored 16 goals across all competitions.[15]
Al-Nassr
On 11 January 2022, Rodríguez joined Saudi Arabia club Al-Nassr.[16]
América
On 20 June 2022, Rodríguez returned to Mexico and joined Club América on a permanent transfer.[17]
