Villalba was born on 26 July 1994 and lived almost to maturity in the Villa 1–11–14. He arrived in San Lorenzo when he was 10, and was chosen after a test in which 500 boys were selected to start a path to professionalism. He confessed to being a fan of San Lorenzo, and went through all the lower levels at the club.

On 18 August 2012, he made his debut in the Primera Division Argentina, against Estudiantes de La Plata, when he entered in the 37th minute of the second half replacing Luis Aguiar, with Ricardo Caruso Lombardi as team manager.

On 22 July 2016, Villaba signed as a young Designated Player with Major League Soccer side Atlanta United. He joined Liga MX side Tijuana on loan on 28 July 2016, but struggled to make many appearances for the club due to injury.

Despite being born in Argentina, Héctor is also eligible to represent Paraguay because his father was born there. On 5 September 2018 Villalba made the one-time switch to Paraguay in hopes of making the squad for the 2019 Copa América and the 2022 FIFA World Cup.

On 25 September 2018 Villalba was called up to Paraguay along with fellow club teammate Miguel Almirón for a national team camp despite not scheduling any friendlies. He made his competitive debut with Paraguay on 20 November as a substitute in the second half of the friendly match against South Africa.

In January 2018, Villalba earned a U.S. green card which qualifies him as a domestic player for MLS roster purposes.

On 31 January 2020, Villaba was transferred to Paraguayan Primera División side Club Libertad for an undisclosed fee.