At club level, he made his debut for América on 4 February 2006 against Atlas. His debut in an international tournament came in 2007, when América participated in the Copa Sudamericana, where they finished runner-up. In 2009 América participated in the World Football Challenge, where he scored in the 2–1 win against AC Milan. In 2011 Esqueda scored against European clubs Manchester City in a 1–1 draw, and against Real Madrid in a 2–3 loss.
Pachuca, Atlas, Tigres UANL, Veracruz and Chiapas FC
On May 23, 2011, he was transferred to CF Pachuca. After several years of injuries and ups and downs with Pachuca, on 2014 he was loaned to Atlas de Guadalajara. Under the command of Tomas Boy, Esqueda scored three goals with Atlas. On 2015, he was transferred on loan to Tigres UANL. With Tigres, he scored a hat-trick in the Copa Libertadores 2015 victory of 5–4 over Juan Aurich on April 15, 2015. He scored the last goal of the 3–0 victory in the Clásico Regiomontano against arch-rival CF Monterrey on April 18. He scored the first goal of the 2–1 victory over Club Universitarioin the round of 16 of the Copa Libertadores 2015 in Bolivia. Post 2015 his career graph substantially dipped due injuries and off form as a process he was out from first XI for most of the time. After winning his first Liga MX with Tigres UANL as a reserve player, Esqueda was loaned out to Tiburones Rojos de Veracruz where he had a discreet stint. In July 2016, Esqueda was loaned out to second division team FC Juarez a move which Esqueda refused to comply with. After an inactive fall 2016 semester, Esqueda was loaned out to Chiapas F.C.. His resentment for Tigres UANL is apparent as he has publicly desecrated the Tigres UANL crest on television. After the disaffiliation of Chiapas F.C., Esqueda became a free agent.
On January 20, 2018, Esqueda began trials with Ekstraklasa club Arka Gdynia. On January 22, he made his unofficial debut with the Polish side in a friendly against Romanian Side Fc Botosani, and scored the 1st goal in an eventual 2–0 win, making Esqueda the 1st Mexican to score for any team in Poland. On February 6, he signed a contract valid for the rest of 2017-18 season, with an extension option.
East Bengal
On 20 August 2018, free agent Esqueda joined Indian I-League club East Bengal for the upcoming season. On 27 October, he made his debut, scoring a brace in a 2–0 victory over NEROCA. He went onto score 9 goals in 14 matches as East Bengal finished 2nd in the I-League, with 3 assists and has been M.O.M. 3 times. He finished as the highest goal getter for East Bengal along with teammate Joby Justin in the 2018-19 I-League season.10 March 2019, Enrique release from East Bengal.
International career
Esqueda was a part of the U-17 world champion team in Peru in 2005. He was also part of the U-20 team that represented Mexico at the 2007 FIFA U-20 World Cup, but was cut from the team at the last minute. He formed part of the U-23 team that was to represent Mexico at the 2007 Pan American Games in Rio de Janeiro, Brazil. He helped Mexico achieve a bronze medal, with him scoring four goals, becoming one of the top scorers of the tournament. He was called up by the Mexico national team for a game against El Salvador. He scored his first goal on 14 October 2009 against Trinidad & Tobago in a 2–2 draw. His most recent appearance was on 3 June 2015 in a friendly against Peru. He was part of the 2015 Copa America roster, however he did not make any appearances during the tournament.
