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Argentina had been thrashed 6-1 by Bolivia when the sides last met in the thin air of La Paz in qualifiers for the 2010 World Cup.
Another upset looked on the cards on Tuesday when Bolivia striker Marcel Martins headed the home side into a 25th-minute lead.
But Argentina -- who had impressed in a 3-0 win over Venezuela in Buenos Aires last Friday -- grabbed a share of the points when Valencia's Ever Banega headed in the equalizer shortly before half-time.
Argentina might even have taken all three points, but captain Lionel Messi squandered a golden chance when one-on-one with Bolivia keeper Sergio Galarza six minutes from time.
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.
In Quito, Ecuador's 4-1 victory over bottom team Paraguay lifted them over Colombia into second, four points behind Argentina.
The day's other match saw 2010 World Cup semi-finalists Uruguay suffer another setback after a 2-0 defeat to Chile in Santiago.
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.
Earlier, Argentina had been slow to adapt to the rarefied air of the Bolivian capital, the world's highest capital city standing some 3,650 meters (11,975 feet) above sea level.
Bolivia, thrashed 5-0 by Colombia in their last outing on Friday, looked far more comfortable as they pressed the visitors relentlessly.
The home side were unlucky not to take the lead after only 10 minutes when only a superb save from Argentine goalkeeper Sergio Romero denied Bolivian Diego Bejaranao a goal.
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.
It looked as if Bolivia would preserve their lead at the break but moments before half-time Argentina grabbed an equaliser.
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.