Argentina opened up Trinidad and Tobago on numerous occasions but wasted a host of chances in Buenos Aires, which may prompt coach Alejandro Sabella to rethink his forward setup.
The hosts unsurprisingly dominated possession and goalscoring chances but they struggled to test Trinidad and Tobago goalkeeper Marvin Phillip often enough, with only five of their 17 shots hitting the target.
Boca Juniors midfielder Fernando Gago made his first appearance since mid-April having missed over a month's worth of football with a knee injury, as Sabella left Sergio Aguero, Gonzalo Higuain and Pablo Zabaleta on the bench.
Gago had injured his left knee against Colon in Argentina's Primera Division on May 13 but declared last month 'the injury is behind me', and the 28-year-old looked comfortable before being replaced at half-time.
Inter's Hugo Campagnaro started ahead of Zabaleta at right-back, while Palacio and Paris Saint-Germain forward Ezequiel Lavezzi were preferred to Aguero and Higuain up front.
A combination of poor decision making and inaccurate shooting was to blame for Argentina's wastefulness at River Plate's Estadio Monumental Antonio Vespucio Liberti, with Sabella's men providing an example of both in the opening 15 minutes.
Although Trinidad and Tobago struggled to get control of the ball for long periods, they broke through the home side's defence a couple of times later in the half, only for Campagnaro and Martin Demichelis to deny Kenwyne Jones with sliding tackles.
Palacio got to Di Maria's corner first at the near post and, although Phillip got both hands to the ball, the visiting gloveman ended up almost throwing the ball into the net.
The goal ended Trinidad and Tobago's run of 313 minutes without conceding.
But Argentina's wastefulness continued with Rodriguez failing to convert a one-on-one opportunity soon after his goal.
Palacio limped off with a potential ankle injury with 14 minutes remaining and could be in doubt for Argentina's final warm-up friendly against Slovenia on Saturday in La Plata.
