In La Paz, Juan Carlos Arce and Marcelo Moreno struck either side of halftime as Bolivia heaped misery on Argentina with a shock 2-0 victory.
In Messi's absence, Argentina coach Edgardo Bauza gave a chance to Atletico Madrid forward Angel Correa, who started in attack alongside Sao Paulo's Lucas Pratto.
A raft of injuries and suspensions meant that Correa was one of eight changes to the Albiceleste team that defeated Chile in Buenos Aires.
With Manchester City forward Sergio Aguero on the bench, Argentina began on the back foot in the rarefied air of Bolivia's Andean capital.
The hosts opened the scoring just after the half-hour mark when Arce met Pablo Escobar's long pass with a header into the bottom-right corner.
Bolivia doubled their lead just after halftime through former Wigan Athletic striker Moreno, who controlled an Enrique Flores cross before rifling a shot past goalkeeper Sergio Romero.
The result left Argentina fifth in the South American zone World Cup qualifying standings with 22 points from 14 matches. Bolivia, who now have 10 points, remained ninth.
Meanwhile, James Rodriguez and Juan Cuadrado were on target as Colombia improved their chances of an automatic qualification place with a 2-0 win over Ecuador in Quito. The hosts were forced to play the final half hour with 10 men after Luis Caicedo was shown a second yellow card for a rash tackle.
In Santiago, Esteban Paredes netted a brace and Alexis Sanchez also scored in Chile's 3-1 defeat of Venezuela. West Bromwich Albion forward Salomon Rondon was on the scoresheet for Venezuela.
Vakifbank player Lonneke Sloetjes spikes the ball during the third-place-final between Vakifbank and Eczacibasi at the 2016-2017 Turkish Women Volleyball League Playoff match in Istanbul Wholesale Green Bay Packers Jerseys , Turkey, on April 30 Wholesale Detroit Lions Jerseys , 2017. Vakifbank won the match 3-1. (XinhuaHe Canling)
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