Messi starred in Thursday's 1-0 win over Ecuador, scoring a stunning 78th-minute free-kick to clinch all three points in Argentina's first qualifying game for the 2026 World Cup.
However, the World Cup winners had to cope without Messi's magic on Tuesday after the Inter Miami forward was left out of the squad due to a knock sustained against Ecuador.
In Messi's absence, Argentina took the lead in La Paz just after the half-hour mark when Angel Di Maria's low cross from the right flank was guided home by Chelsea midfielder Enzo Fernandez.
Bolivia had lost their previous five World Cup qualifiers, and their hopes of claiming a positive result were dashed by Roberto Fernandez's reckless challenge on Cristian Romero.
The 24-year-old was shown a straight red card for a studs-up challenge on the Tottenham Hotspur defender, ensuring Bolivia played the remainder of the contest with 10 men.
La Albiceleste quickly made their numerical advantage count, doubling their lead just before the half-time break through Lyon defender Nicolas Tagliafico.
Di Maria registered his second assist of the first period when his deep free-kick was calmly headed home by Tagliafico, who celebrated his first international goal.
With Argentina in complete control, Nicolas Gonzalez wrapped up the three points in the 83rd minute, driving a near-post strike past Bolivia goalkeeper Guillermo Viscarra.
As a result of the comfortable victory, La Albiceleste are now unbeaten in their last 23 World Cup qualifiers — a run which stretches back to 2017.
Lionel Scaloni's side will return to qualifying action in October when they face Paraguay in Buenos Aires, before travelling to Lima for a meeting with Peru.