Héctor Moreno joined Club Universidad Nacional’s youth system in 2003 at age 15, and made his way into the first team after winning the FIFA U-17 World Championship with Mexico in 2005.

On 13 December 2007, it was announced Moreno was transferred to Dutch club AZ in a US$4.5 million deal. He made his Eredivisie debut on 1 March 2008 in a 1–1 draw against Roda JC, playing the full 90 minutes. In April 2009, Moreno won his first Eredivisie title with AZ. On 22 April, it was reported Moreno had signed a contract extension with AZ which would tie him to the club until 2014.

Moreno made his Mexico senior team debut on 17 October 2007 under Hugo Sánchez in a friendly against Guatemala.

On 25 July, AZ won the Johan Cruyff Shield after defeating Heerenvecen 5–1 in the final. Moreno made his debut in the UEFA Champions League on 16 September in a 0–1 defeat to Olympiacos. On 7 February 2010, Moreno gave Alkmaar a 2–1 victory over Feyenoord by scoring a header from a corner-kick in the 87th minute. He scored his third goal of the season in a 6–2 victory over RKC Waalwijk on 13 March 2010. He would score his fourth goal in a 3–0 victory over Willem II on 18 April.

Moreno was included by Javier Aguirre to be a part of the 23-man squad that would participate in the 2010 FIFA World Cup. He made his debut in the Group A match against France on 17 June, which Mexico won 2–0. Moreno would also start against Uruguay.

On 22 June 2011, it was announced Moreno would transfer to Spanish La Liga club Espanyol on a five-year contract for an undisclosed fee. On 28 August, he made his debut in La Liga against Mallorca. On 26 September, he scored his first goal in a 1–3 loss to Levante. On 3 December, he would score his second league goal in a 1–2 loss to Valencia. Moreno scored his third goal of the season in a 3–1 home win against Racing de Santander.

On 4 October 2012, Moreno was named Espanyol’s Player of the Year for the 2011–12 season, his debut season, playing 35 league matches (for a total of 3,295 minutes played) and scoring three goals with one assist.

On 12 June 2012, Moreno the winning goal for Mexico in a 2–1 over El Salvador in a 2014 World Cup qualifying match, the first of his career.

On 5 June 2014, national team coach Miguel Herrera named Moreno in the final 23-man squad for the 2014 World Cup. On 29 June, in the round of 16 match against the Netherlands, Moreno suffered a fractured tibia after a collision with Dutch striker Arjen Robben inside his own penalty area. Moreno was stretched off the field a few minutes before half-time and was substituted by Diego Reyes. It was later reported Moreno was expected to be ruled out of action for up to six months.

On 15 August 2015, PSV announced the signing of Moreno. Upon his return to the Eredivisie, Moreno signed a four-year contract for €5 million with the club.

On 27 June 2015, during Mexico’s friendly match against Costa Rica, Moreno was substituted off at half-time after complaining of pain. On 1 July, the Mexican Football Federation announced Moreno would be ruled out of the upcoming 2015 CONCACAF Gold Cup tournament after a successful surgery on his right foot, which stemmed from complications related to a procedure he underwent six years prior following an injury to his fifth metatarsal. He was replaced in the squad by Oswaldo Alanís.

On 17 January 2016, Moreno scored in PSV’s 2–0 win over Feyenoord. A week later, he scored his first double as PSV defeated Twente 4–2 with assists provided by fellow Mexico international teammate, Andrés Guardado.

In May 2016, he was called up for the Copa América Centenario by Juan Carlos Osorio.

On 13 June 2017, Moreno joined Italian side Roma on a four-year contract. He made his Serie A debut on 16 September in Roma’s 3–0 win over Hellas Verona, replacing Kostas Manolas in the 73rd minute.

On 31 January 2018, Spanish club Real Sociedad announced the transfer of Moreno from Roma for €6 million, signing with the club until 2021. On 15 February, he made his competitive debut for La Real against Red Bull Salzburg in the Europa League, playing 76 minutes in the team’s 2–2 draw. During midweek training, however, Moreno suffered a grade 1 injury to his internal obturator, meaning he would be ruled out for an undisclosed period of time. He returned and made his debut in La Liga with Real Sociedad on 1 March in a scoreless draw against Real Betis. Three days later, he scored his first goal against Deportivo Alavés, giving his team the lead at the 6th minute, in an eventual 2–1 victory.

In May 2018, he was named in Mexico’s preliminary 28-man squad for the 2018 FIFA World Cup in Russia, and in June, was named in Mexico’s 23-man squad for the 2018 FIFA World Cup. He would appear in all group stage matches but accumulated two yellow cards during the group stage, making him miss out on the round-of-16 0–2 loss against Brazil.

He transferred to Al-Gharafa in July 2019, making him the first Mexican international player to play in Qatar Stars League. He made his debut the following month on 22 August in a 3–0 victory over Al-Shahania. On 9 November, he would score his first goal for the team in a 2–0 victory over Umm Salal SC.

On 6 June 2019, Moreno was called up by coach Gerardo Martino to participate in the CONCACAF Gold Cup. Three days later, in a warm-up match against Ecuador, he would pick up an injury following a clearance. He would return to the field on 29 June in the quarter-final match against Costa Rica, coming in as an overtime substitute at the 106th minute and managing to score in the penalty shoot-out. On 2 July, Moreno played his 100th match with Mexico against Haiti, in a 1–0 win in the semi-finals of the Gold Cup. The team would go on to win the tournament, defeating the United States 1–0 in the final.