Gómez started his club career in his home country with Arsenal de Sarandí, before joining San Lorenzo in 2009. The following year, he was signed by Italian club Catania. In 2013, he joined Ukrainian side Metalist Kharkiv, where he remained for a single season, before returning to Italy to play for Atalanta. In 2019–20, Gómez set the Serie A record for most assists in a single season with sixteen, and was named to the Serie A Team of the Year.