Born in Vichadero, Álvez came up from River Plate´s youth system, but failed to appear as a senior with the first team. In 2008, he moved to Segunda División side Boston River, scoring his first senior goal on 29 November of that year in a 1–0 home win against Rocha. In September 2009, Álvez joined Coraceros Polo Club in the Segunda División Amateur, and scored 13 goals for the side; highlights included a hat-trick in a 3–1 away win against Albion. He subsequently signed for fellow league team Platense, contributing with nine goals and narrowly missing out promotion. In 2011, Álvez agreed to a deal with Torque, still in the third division. He achieved promotion to the second level in his first season as champions, and scored a 17 goals as his side missed out a consecutive promotion in the play-offs. In February 2012, Álvez moved to Toluca with Torque teammate Nicolás Milesi on a trial basis, but nothing came of it. On 19 June 2013, he agreed to a one-year loan deal with Danubio. Álvez made his Primera División debut on 18 August 2013, starting in a 0–0 away draw against Cerro Largo. On 14 September he scored his first goal in the category, netting the first in a 2–0 home win against Nacional. Álvez scored 15 goals for Danubio during his spell, including two braces against Fénix and one against Racing Montevideo.
On 16 August 2014, Álvez moved abroad for the first time in his career, signing a one-year loan deal with Primeira Liga side Vitória Guimarães. He made his debut on 30 August, replacing Tomané in a 3–0 away win against Belenenses. Álvez scored his first goal abroad on 19 September 2014, netting the equalizer in a 1–1 home draw against Paços de Ferreira. On 3 October, he scored a brace in a 3–0 home win against Boavista. Álvez scored five goals for Vitória, but left the club in June 2015 after failing to agree new terms.
Ecuador
On 26 July 2015, Álvez signed for LDU Quito until the end of the year. He scored ten goals for the side in only 18 matches, as his side finished second after losing the finals to Emelec. On 10 February 2016, Álvez was presented at Barcelona SC after agreeing to a four-year deal. In his first season, he scored 19 goals as his side was crowned champions.
