Lionel Scaloni’s side were on course to reach the last-four in regulation time after Lisandro Martinez’s opener on 35 minutes looked to have sealed a narrow victory as the clock ticked past 90 minutes.
However, Kevin Rodriguez’s header in the first minute of stoppage time forced the game to spot-kicks where the reigning FIFA World Cup winners prevailed – with the Blues’ forward dispatching from 12 yards.
It means Argentina will face Venezuela or Canada on Wednesday 10 July for a place in this year’s showpiece at Hard Rock Stadium, Florida.
The clash at NRG Stadium started at a frenetic pace with both sides creating chances before Jeremy Sarmiento and Kendry Paez both came close to an opener for Ecuador with the former denied by Emiliano Martinez from close range and the latter firing over the bar.
The world champions then grew into proceedings and came agonisingly close to the breakthrough when Nahuel Molina’s cross was met by Enzo Fernandez whose header glanced just wide of the post.
That would signal the start of continued Argentina pressure which paid off on 35 minutes when Martinez directed Alexis Mac Allister’s corner into the net which – after a VAR check – was awarded.
The defender’s goal represented the first half’s only, and Ecuador were given a golden chance to level 15 minutes after the interval when the referee – with the aid of VAR – awarded a penalty after Rodrigo de Paul appeared to handle in the area.
Enner Valencia stepped up, but could only send his attempt from 12 yards crashing off the post.
It appeared Ecuador would rue the opportunity when the clock ticked down with Argentina holding their slender lead, but Rodriguez’s last-gasp header in second-half stoppage time forced the encounter to penalties.
Lionel Messi’s opening effort crashed against the crossbar but the Inter Miami forward’s blushes were spared by Martinez, who so often plays a starring role in shootouts, saved Angel Mena’s attempt.
Alvarez then unleashed an unstoppable effort before Aston Villa’s keeper produced another fantastic stop to deny Alan Minda.
Argentina’s Mac Allister and Gonzalo Montiel and Ecuador’s John Yeboah and Jordy Caicedo’s finishes meant former City man Nicolas Otamendi could win the shootout with his nation’s final kick.
And the defender made no mistake to send Scaloni’s men into the semi-finals with a 4-2 penalties win.
