La Albiceleste were forced to go through the lottery of penalties after Kevin Rodriguez's stoppage-time equaliser cancelled out Lisandro Martinez's 35th-minute strike.
Lionel Messi overcame a hamstring issue to play the duration of the contest before he stepped up to take the first penalty of the subsequent shootout.
The Inter Miami forward ultimately fluffed his lines, with his Panenka attempt clipping the crossbar to give Ecuador an early advantage.
However, Martinez swiftly demonstrated why he is a penalty-shootout specialist, making consecutive stops from Angel Mena and Alan Minda to turn the shootout back in Argentina's favour.
Martinez maintains unbeaten penalty record
While Ecuador scored their next two spot kicks, Argentina netted four of their five penalties to emerge victorious at the NRG Stadium in Houston.
Not only did he help his side progress to the next round, but Martinez also maintained his 100% record in international penalty shootouts.
Argentina have now won all four shootouts in which Martinez was in goal, including his first success in the semi-finals of the 2021 Copa America against Colombia.
The Aston Villa goalkeeper then helped Argentina prevail on penalties in the quarter-final and the final of the 2022 World Cup against the Netherlands and France respectively.
Martinez "proud" of shootout success
After pulling off more penalty heroics, the 31-year-old admitted he was not prepared to go home in the quarter-final stage.
"I dive 500 times a day in every training session to be able to perform," Martinez told reporters. "I work for this, I always try to be at my best level to give everything for this national team.
"I am proud, happy for all this. I told the guys I wasn't ready to go home. Even though we are world champions and Copa America holders, this group deserved to continue.
"We have been here for 35 days, fighting for this. I am happy we have progressed. They played a great game, very physical. We knew they would be one of the toughest rivals in the Copa America."
After prevailing against Colombia in 2021, Argentina have now won two consecutive Copa America penalty shootouts for just the second time - a feat they previously achieved against Brazil and Colombia in 1993.
Despite that success, Lionel Scaloni will hope his side can progress in regulation time when they face either Canada or Venezuela in Tuesday's semi-final.