Ecuador's Antonio Valencia had his side's best chance with a header that hit the post while Argentina came closest with a volley two minutes from time by substitute Maxi Rodriguez that also came back off the woodwork.
Ecuador were the dominant side in the first half creating several good chances as Argentine tried to settle with full backs Facundo Roncaglia and Lucas Oran winning their first caps.
"The two worked hard and had difficulties where Ecuador are strong," Argentina coach Alejandro Sabella said. "When Messi isn't there we feel his absence."
Messi will be out for between six and eight weeks with a hamstring injury suffered in Barcelona's match against Real Betis on Sunday.
The nippy Jefferson Montero gave Roncaglia a tough debut and beat his man in the 12th minute to cross to the far post where Valencia's header hit the post.
Argentina played deep in the first half, defending in numbers against the quick counter-attacks launched by Ecuador down the flanks, and strikers Gonzalo Higuain and Ezequiel Lavezzi saw little quality ball.
Argentina, captained by Javier Mascherano, pushed their midfield further up after the interval and took charge with Angel Di Maria having four shots on goal in the opening 10 minutes of the second half.
Sergio Aguero came on in the 62nd minute for Lavezzi and gave Argentina's attack more bite before Rodriguez, who scored Argentina's last two goals against Uruguay last month, hit a first time volley from two metres out against the post.
Argentina play Bosnia in St. Louis on Monday and Ecuador meet Honduras on Tuesday.