Martins handed the Verde an early lead, but the hosts were thwarted by Ever Banega, who ensured a share of the points.
Marcelo Martins repeated his scoring exploits in that infamous 6-1 destruction from 2009 to put the home side ahead, but Ever Banega responded with a well-taken header to avoid defeat for an uncharacteristically cautious Argentina.
Returning to the site of one of their worst results in history, Argentina came out with a tenuous outlook, trying to keep hold of possession early and absorb Bolivia's attacks, while waiting patiently to counter. The long grass of La Paz's Hernando Siles stadium, however, was not conducive to keeping the ball on the ground, and Alejandro Sabella's men struggled early on to compete against fearsome pressing from the home team.
The CONMEBOL leader had an early scare when Alejandro Bejarano evaded his markers, appearing at the far post. The fullback controlled a cross-field pass, but could not flick the ball over Argentina goalkeeper Sergio Romero with men waiting in the middle.
At the other end, the Albiceleste demonstrated that if given space, they could be devastating going forward. Brilliant play on the counter from Lionel Messi and Angel Di Maria left Rodrigo Palacio clean through with Sergio Galarza, but the Inter man failed to beat the Bolivia No. 1, who saved with his feet.
The Verde never stopped attacking their illustrious rivals, though, and were rewarded after 25 minutes with the opening goal. Alejandro Chumacero left Clemente Rodriguez standing on the right wing, and a well-placed cross found Marcelo Martins, who powered a header past Romero.
To their credit, Sabella's charges raised their game after the goal. Di Maria was guilty of missing a clear header from close range, but he almost redeemed himself with a wonderful individual effort. The Real Madrid man combined well with Gino Peruzzi before setting off on a lung-busting run in the La Paz altitude, and his shot from outside the area flew just wide of Galarza's left post to deny him a great strike.
Just when Argentina appeared certain to start the second half from a losing position, another clinical counter finally bore fruit. Javier Mascherano kick-started the break with a fine lofted pass, and Messi held on to the ball just long enough to find the overlapping Rodriguez. Clemente appeared to have stumbled on the uneven pitch, but he recomposed himself to flight the ball to the edge of the area, where Banega managed to get down and connect with a header that somehow crept past Galarza and into the net.
With just more than five minutes left, Messi looked certain to hit his first against Bolivia and seal three points, after breaking through with nobody to beat but Galarza. The away fans were already celebrating, but the Barcelona forward's usually-deadly aim failed him and he was foiled by the keeper, sealing a share of the spoils that nevertheless left Argentina content.
The draw leaves both sides in the positions they occupied before kickoff, Argentina extending its lead at the top over Colombia to five points albeit having played two more games. Bolivia, meanwhile, stays second from the bottom with just nine points from its 11 qualifying clashes.