But despite remaining top of the CONMEBOL group Argentina saw their lead cut to three points by Colombia who had earlier beaten Peru 2-0.
Ecuador, meanwhile, remain third on 21 points, five less than the Albicelestes.
Even though the effects of playing at high altitude - 2,800metres above sea level - could have hampered the visitors they began the game with an attacking outlook.
The opening goal came in the third minute of the game when Angel Di Maria's shot was parried by goalkeeper Alexander Dominguez who then fouled Rodrigo Palacio as they both went for the loose ball.
Sergio Aguero beat Dominguez from the penalty spot for his fourth goal in the current World Cup qualifying campaign.
Alejandro Sabella's side did not press their advantage and instead tested the Ecuador defence with long-range shots.
The hosts equalised in the 16th minute when Segundo Castillo headed a free-kick into the back of the net.
Di Maria was the most threatening Argentinian player in the first period but Dominguez was equal to his efforts.
Sabella brought on Lionel Messi for Aguero for the last 20 minutes and Argentina took control of the game.
The Barcelona forward had two chances - the first saw him connect with a Rodrigo Palacio pass but his shot was deflected and the next was just wide of the post.
Midfielder Javier Mascherano was shown red with four minutes to go after he became frustrated by Ecuador players taking their time over receiving treatment.
Jorge Guagua had the last opportunity of the game but sent his header off target in injury time.
Argentina centre back duo Federico Fernandez and Ezequiel Garay are banned for the next qualifier against Paraguay after they were both shown a second yellow card of the competition during the game with Ecuador.