Raul Jimenez opened the scoring midway through the first half with a superb long-range free kick that soared over the US wall and angled into the top-right corner to the delight of fans at Estadio Akron.
El Tri took firm control of the match early in the second half when the ball fell to Cesar Huerta in front of goal and he whipped a quick shot past diving US goalkeeper Matt Turner to double their advantage.
It was a much-needed victory for Mexico after they were booed by fans following a disappointing 2-2 draw in a friendly last weekend against an under-strength Valencia.
The US, who beat Panama in Pochettino's debut on Saturday, were short on firepower with Christian Pulisic, Ricardo Pepi and Weston McKennie among those who did not make the trip to Mexico and instead returned to their club sides.
Absences aside though, it was still an uninspired and passive performance from the US, who had just one shot on target and saw their seven-match unbeaten streak against their fierce rivals come to an end.
Pochettino said the US started strong but the game changed after Mexico's first goal.
"It wasn't a great performance but this type of game is perfect for us to learn," the Argentine told reporters.
"Overall I think Mexico was a little bit better than us and fully deserved the victory, but for us, it is a process."
The match also marked the emotional farewell of Guadalajara-born Andres Guardado, Mexico's most-capped player, who left the field to a standing ovation when he was subbed early in the first half after earning the last of his 182 caps.
