Argentinian keeper Emiliano Martinez had his own work to do, making a smart low save at the end of the first half before tipping a looping header over the bar as Indonesia pressed for an equaliser.
But Argentina made their pressure count, denting any Indonesian hopes on 55 minutes when Tottenham defender Cristian Romero lost his man to thump home a header.
Argentina were without several other first-choice regulars in Jakarta, including Juventus midfielder Angel Di Maria and Benfica defender Nicolas Otamendi.
They beat Australia in another friendly in Beijing last week, with Messi scoring the quickest goal of his career in a 2-0 win.
Bringing Argentina to Jakarta for the first senior international match between the two sides cost the Indonesian football association as much as US$5 million, according to local media.
Indonesians did not get a glimpse of Argentina’s modern-day superstar Messi but they were happy to see the world champions play their hometown heroes.
“If Messi came, we would be more excited,” said Fahri Satria, a 30-year-old tourism worker.
“But it’s okay.”