The Albicelestes were thrashed 6-1 on their last visit to La Paz four years ago and they looked set for another uncomfortable evening in the high altitude as Bolivia took a 25th-minute lead through Marcelo Martins.
However, Ever Banega levelled things up on the stroke of half-time and Argentina would go onto dominate the second half before having to settle for a draw which moves them onto 24 points from 11 games at the top of the South American qualifying group.
Argentina's crushing defeat at the Hernando Siles stadium, located at more than 3,100 metres above sea level, during qualifying for the 2010 World Cup was a major humiliation but they would have been optimistic of avoiding a repeat this time, lying 15 points above second-bottom Bolivia in the standings at kick-off.
However, Alejandro Sabella's side struggled at the start and found themselves on the back foot as Bolivia took control.
The hosts were unable to make anything of their early dominance though and Argentina created the first real chance of the match when Lionel Messi and Angel Di Maria launched a counter-attack that led to Rodrigo Palacio being put clean through.
He was not able to take advantage of that opportunity, though, and Bolivia were not so profligate soon after when Martins, who also scored the opening goal in that 6-1 win, headed home a long ball from Alejandro Chumacero.
That was a blow for Argentina but they responded well and were on level terms before the break when Banega nodded home Clemente Rodriguez's ball in.
Buoyed by that goal, the visitors went in search of a winner in the second period and it was only the fine performance of home goalkeeper Sergio Galarza that prevented them getting all three points.
The veteran keeper did superbly to keep out long-range shots from Banega and Messi, and then with the final whistle approaching he again denied Messi after the Barcelona superstar had been given a late chance.
Messi admitted he found the conditions tough and prevented him from playing as he normally would hope to.
He said: "It is very hard to play here. I have several problems and I knew that I had to take care of my stamina. I could not run as usual."
His team-mate Sebastian Dominguez echoed those thoughts and said Argentina were happy with the point.
"We know that it's always hard at this ground. It takes a lot out of us and we have to make a stronger effort to be equal to them, as they are used to it," the defender said.
"It is not an excuse, it's science. However, we managed to get an important point. We have to be satisfied."