Funes Mori was born in Mendoza, Argentina. In 2001, he moved to Workman Junior High and Arlington High School where he was coached by the Brazilian Coah Rocha, playing football with his twin brother, Ramiro. The twins' father, Miguel, played professional football in Argentina with clubs such as Independiente Rivadavia and Club Atlético Argentino in the 1980s. Funes Mori scored 40 goals in the 2008 season leading his team to District Champions and Area Finalist with a record of 24–2–1. Gabriel and Ramiro, who are identical twins, also played several seasons for the Associated Soccer Group 91' team. His coach with ASG was Uche Okafor. After that, Chelsea scout Jorge Alvial scouted Rogelio and Ramiro on the first day of the reality showSueño MLS, and spoke to his parents about a future tryout at Chelsea. He participated in Sueño MLS and won the contest, therefore becoming part of FC Dallas.
Funes Mori began his professional career with River Plate in the Argentine Primera División on 6 December 2009, on a 1–3 defeat against Vélez Sársfield. He played the last two games of that year at home against Racing Club and away to Tigre, scoring his first goal with the club in their visit to the latter. In the traditional pre-season encounters for the big clubs in Argentina, the Torneos de Verano, he scored for River in a 3–1 victory over their rivals Boca Juniors in Mar del Plata's Copa Desafío. On 9 May, during the 2010 Clausura tournament, he scored his first hat-trick for River Plate in a game against Racing Club. He achieved the three goals in only 24 minutes, breaking a personal 11-match streak without scoring a goal. In the last game of the tournament, the forward scored River's only goal in a 1–5 loss to Tigre at home. In the first game of the 2010 Apertura, he scored a 90th-minute goal following an assist from Ariel Ortega to secure a 1–0 victory over Tigre. This was his third goal in three games against that team. In the third fixture, against Independiente, he scored two goals in the first half as River went on to win 3–2. The forward scored his fourth goal of the season in the 1–0 victory over Arsenal de Sarandí.
On 10 August 2013, Funes Mori joined Benfica on a five-year contract. River Plate received €2 million from an investment group who kept a share of its economic right's, with Benfica receiving half, plus the sports rights. On 15 September, he made his debut for Benfica B, scoring his first goal in a Benfica shirt. On 15 March, he scored four goals for the B side against Sporting Covilhã in a 4–0 win. On 9 July 2014, he was loaned to Eskişehirspor in Turkey for one year, with the option to make the move permanent for a €3.5 million fee.
Monterrey
On 12 June 2015, Funes Mori moved to Mexican club C.F. Monterrey. He made his debut in a 3–2 friendly win over Morelia, scoring in the 91st minute. He is currently the club's 2nd all-time top scorer behind Humberto Suazo, who has 121 goals.
