He began his career at Ferro Carril Oeste, signing for Sevilla in 2007. He made 201 official appearances for the latter club in nine years and scored 15 goals, joining Tottenham Hotspur in August 2014.
Born in Buenos Aires, Fazio started his career in the Primera B Nacional with Ferro Carril Oeste in 2005. He was bought by Spanish club Sevilla FC in late January 2007 and spent the vast majority of the remaining season with the reserves, which he helped achieve promotion to Segunda División.
Fazio started 2007–08 registered with both Sevilla teams. However, due to the absences of Javi Navarro (knee, entire campaign missed) and Julien Escudé (pubis, less than half of possible games), he ended up playing an important part on a side that reached a final qualification to the UEFA Cup. His first game with the main squad was on 25 August 2007 in the season opener, a 4–1 home La Liga win against Getafe CF.
On 7 May 2008, Fazio scored his first goal for Sevilla in a 3–0 win at Racing de Santander. He added another in that match, and a third a week later in a 2–0 home success against Real Betis; in both games, he played as a defensive midfielder.
In his second year, they finished third but Fazio featured slightly less and saw time at both positions. He was mostly injured during the following season, playing only ten league contests (on 13 March 2010, he headed home in a 1–1 home draw against Deportivo de La Coruña); the Andalusians ended the league in the fourth place, also winning the Copa del Rey, but he was not picked for the final of the latter competition itself.
Still bothered with some physical problems in 2010–11, Fazio played the most he had in years, appearing in 19 games – 17 starts – as Sevilla ranked fifth and qualified to the Europa League.
On 26 August 2014, Fazio signed for Tottenham Hotspur for a fee of £8 million, on a four-year contract. On 18 October he started on his Premier League debut at Manchester City, but was given a straight red card for denying Sergio Agüero a goalscoring opportunity in the penalty area, in an eventual 1–4 defeat. On 6 November he met the same fate, after conceding a penalty with a foul on Jerónimo Barrales in the closing stages of a 2–1 away win over Asteras Tripoli F.C. for the Europa League group stage.
On 31 January 2016, after only one competitive game in the first part of the season (a 1–2 home loss against Arsenal in the League Cup) Fazio returned to Sevilla on a five-month loan. He was sent off after just 24 minutes on his debut for two bookable offenses, in a 1–1 away draw to Celta de Vigo; the decision to hand him the number 16 shirt was controversial, as convention had previously been for homegrown players to wear the number that Antonio Puerta bore when he died playing for the team in 2007.
On 3 August 2016, Fazio was loaned to A.S. Roma with the Italians having the possibility of making the deal permanent at the end of the campaign for €3.2 million. He made his Serie A debut 17 days later, playing ten minutes in a 4–0 home win against Udinese Calcio.
Fazio was an integral part of the Argentina under-20 team that won the FIFA World Cup in 2007. The following year he helped the Olympic team win gold at the Summer Olympics, in Beijing: he played twice in the tournament, as backup for Nicolás Pareja and Ezequiel Garay.
On 1 June 2011, Fazio made his debut for the full side, appearing in a 1–4 friendly defeat in Nigeria. He scored his first goal for his country in another exhibition game, netting the opener in an eventual 6–0 win in Singapore on 13 June 2017.As of 21 May 2017
As of 13 June 2017
(Argentina score listed first, score column indicates score after each Fazio goal)
Segunda División B: 2006–07
Copa del Rey: 2009–10
Supercopa de España: 2007; Runner-up 2010
UEFA Europa League: 2013–14, 2015–16
UEFA Super Cup: Runner-up 2014
Football League Cup: Runner-up 2014–15
FIFA U-20 World Cup: 2007
Summer Olympics: 2008