Gómez began his career playing with the youth squad of Argentine side Arsenal de Sarandí, debuting for the team in 2003. Two years later, he was officially called up to the first team, but did not feature as a regular with the side until the 2006 Torneo Apertura, during which he scored 2 goals in 15 appearances, as Arsenal finished the season in 5th place.
On 30 November 2007, Gómez scored the 2 most important goals up to that point of his career in the first leg of the Copa Sudamericana Finals, away against favourites Club América of Mexico's Liga MX, giving Arsenal a valuable 3–2 lead going into the second leg. Arsenal lost the 5 December return leg 2–1, but won their premier championship on the away goals rule.
San Lorenzo de Almagro signed Gómez for a 2 million dollar transfer fee, half of his estimated market value, in time for the 2009 Clausura tournament. His impressive play, including netting 8 times in 48 appearances for Los Santos, attracted the attention of several high-profile scouts. This led to his transfer to Italian Serie A Catania in July 2010, for €3 million.
Catania officially welcomed their new 22-year-old signing on 21 July 2010, and he made his first appearance with the club 9 days later in a 1–0 friendly win against Greek side Iraklis. Gómez was immediately inserted into the starting XI and soon became integral to his club's record-breaking renaissance over the next 3 seasons.
El Papu contributed 4 goals and 5 assists in each of his first 2 seasons. His breakthrough campaign came during the 2012–13 season, when his playmaking and offensive prowess became the main catalyst of the team, propelling his side to club record highs for home and overall victories, and, for their 5th successive year, points. The Rossazzurri clinched an eighth-place finish in Serie A, equaling their historic best placement in the league for the first time since the 1964–65 season, but 5 points shy of earning their inaugural appearance in the UEFA Europa League. The side that managed to achieve these record-breaking achievements was described as the best Catania side in the club's history. Gómez finished the year with a career high 8 goals in 36 appearances, making him the second highest on the team behind Gonzalo Bergessio, as well as 7 assists, making him the club's joint highest assist provider, and the tenth best provider in Serie A.
Catania, for reasons that were never clarified, sold Gómez during the summer and replaced him with the injury-prone and inconsistent Sebastián Leto, whom they acquired on a free transfer from Panathinaikos. Despite having four of their top six offensive players return, and later five of their six when Francesco Lodi was reacquired on loan from Genoa in January, Catania's performances declined heavily, which saw them fall to 18th position in the league, and as a result, they were ultimately relegated.
Rebuffing offers from several big clubs, including Atletico Madrid, Fiorentina, and Inter Milan, Gómez himself requested a transfer to little known Metalist Kharkiv of the Ukrainian Premier League citing the Club's commitment to growth and the opportunity to play in the upcoming UEFA Champions League as his reasons. On 2 August 2013, he signed four-year contract with the club, which included a €12 million release clause, following a €7 million transfer fee. However, things did not go well for him with the side from the beginning.
UEFA upheld Metalist's ban from the Champions League two weeks later because of the club's involvement in match fixing in 2008. By the December winter break, failing to settle into his new surroundings due to a combination of the League's lack of visibility and quality, which he believed made playing in it a waste of time, as well as adverse environmental and linguistic issues in Ukraine itself, which he saw as insurmountable, Gómez wanted out of his contract. He therefore requested a transfer back to Serie A as soon as possible, preferably to Fiorentina, and by January 2014, offered to accept a salary reduction in order to have this accomplished. This request went unfilled, however, and he ultimately played in 23 games, scoring 3 goals and setting up 4 others, helping the Hor'ky finish 3rd overall.
Gómez refused to return to Ukraine the following season because of the volatile and violent political climate that emerged during his time there. He stated 'It’s an anguished situation, very unstable, as we are all sad and living in a state of panic...I have no intention of coming back...I will stay in Buenos Aires...Until there can be guarantees of safety, I cannot expose my family to these dangers.' Many players, especially foreign ones, also left the League for this same reason, including three of Gomez's teammates, and six from reigning league Champions Shakhtar Donetsk. As a result, the Ukrainian League saw its foreign player total reduced from 170 to 60 over the next 2 years.
Atalanta acquired Gómez on 1 September 2014, signing him on a three-year deal. Gómez had a decent first season, contributing 3 goals and 2 assists in 24 appearances to a poor, offensively-challenged Nerazzurri squad that struggled and narrowly avoided relegation, finishing fourth from the bottom, 3 points ahead of Serie B-bound Cagliari.
The following season, Papu lead his club in both goals and assists, with 7 and 6 respectively, as he rekindled the form he had shown in his final season at Catania, and, despite the continued lack of attacking support, steered Atalanta to a respectable 13th-place finish in the league. His performances spurred the interest of several big clubs, which pushed the Bergamese side to extend his contract until June 2020, on 4 February 2016.
In 2007 Gómez was picked to represent the Argentina Under-20 team at the 2007 South American Youth Championship in Paraguay. Later that year he was part of the Argentina squad that won the 2007 FIFA U-20 World Cup in Canada.
Having only played internationally for Argentina at youth level, dual citizenship was widely believed to have qualified him for selection to the senior Italian national team, for whom he had expressed interest in playing. FIFA has since ruled him ineligible to switch his football nationality, however, because he did not have a dual passport when he first represented Argentina at that level, and does not have Italian lineage, which would have allowed him to override this requirement.
On 19 May 2017, Gómez received his first senior call-up by newly appointed coach Jorge Sampaoli for Argentina's friendlies against Brazil and Singapore in June. He made his senior international debut in the match against Singapore on 13 June, helping Argentina to a 6–0 away win, and also marked his debut by scoring his first international goal.As of 22 September 2017
Scores and results list Argentina's goal tally first.
Arsenal de Sarandí
Copa Sudamericana: 2007
Suruga Bank Championship: 2008
FIFA U-20 World Cup: 2007
Superclásico de las Américas: 2017