Another upset looked on the cards on Tuesday when Bolivia striker Marcel Martins headed the home side into a 25th-minute lead.
Despite the failure to take maximum points, Argentina remain in control of the South American qualifying standings after Colombia, who had started the day in second place, crashed 1-0 to Venezuela in Caracas.
The loss leaves Uruguay two points adrift of the qualifying places in South America. The first four teams qualify automatically for Brazil, while the fifth placed team goes into a play-off with their Asian counterpart.
Bolivia open with intensity
Xavier Azkargorta's side pressed Argentina relentlessly from the kick-off and were unlucky not to take the lead after only 10 minutes when only a superb save from Sergio Romero denied the home team's Diego Bejaranao.
Argentina's best efforts came on the counter-attack, but Inter Milan's Rodrigo Palacio wasted a clear chance on 19 minutes when played in by Angel Di Maria, starting in place of the suspended Gonzalo Higuain.
Bolivia continued to carve out openings and Carlos Saucedo should have done better in the 20th minute when he steered a free header over the bar.
Edward Zenteno then tested Romero with a thumping long range effort that the Sampdoria keeper punched behind.
Moments later however Bolivia got the goal their energetic early play had been threatening.
A superb cross from the right flank by Alejandro Chumacero picked out Martins and the 25-year-old wrong-footed Romero with a header back across goal to make it 1-0.
The goal stung Argentina into life but Di Maria squandered a good chance on 35 minutes when his header from a Palacio cross drifted aimlessly wide.
Boca Juniors fullback Clemente Rodriguez found space down the left and chipped a cross into a crowded area for Banega to head home.
Argentina steadied themselves in the second half and hung on for a share of the points.