A tight clash came to life after the break at SDCCU Stadium in California in Martino's first game in charge of Mexico.
A Raul Jimenez penalty and goals from Hector Moreno and Hirving Lozano in the space of 13 minutes put Martino's side in control after Chile had enjoyed the better of the first half.
Nicolas Castillo pulled a goal back for Chile, but Mexico made sure Martino's start at the helm was a winning one.
The early chances for both teams came from set-pieces, and it was Chile who almost opened the scoring in the 14th minute.
Charles Aranguiz's delivery from the right was met by Arturo Vidal, whose good header was saved by Guillermo Ochoa.
Mexico enjoyed some decent moments going forward, but they lacked a final pass throughout the first half.
Chile looked the more likely to open the scoring and only a last-ditch clearance from Moreno denied Castillo midway through the first half.
It was a far livelier start to the second half as Vidal blazed over from inside the area for Chile.
Jimenez almost opened the scoring for Mexico in the 50th minute, the forward managing a shot that hit the post after perfectly timing a tackle on Gary Medel.
However, Carlos Salcedo was fouled inside the area from a set-piece just moments later and Jimenez stepped up to send Gabriel Arias the wrong way from the penalty spot.
Mexico doubled their lead in the 64th minute, Moreno heading in a corner from Andres Guardado.
Just a minute later and it was 3-0, a bad turnover by Chile punished when Rodolfo Pizarro played in Lozano, who chipped a lovely finish over the onrushing Arias.
Chile pulled a goal back with just over 20 minutes remaining, Castillo sweeping in a cross from Eugenio Mena from the right.
However, amid a flurry of late substitutions, the game somewhat lost its rhythm, allowing Mexico to see out their win despite Javier Hernandez having a late strike ruled out for offside.
What does it mean? A win's a win for Mexico
Mexico came into the friendly on the back of seven losses in their past eight games. While Martino will expect improvement from his team, a win should at least lift confidence after what has been a difficult run dating back to the World Cup.
Still work to do for Martino
Mexico were perhaps fortunate not to fall behind in the first half as Chile pushed. However, they had some good moments – particularly in transition – but were often let down by their final pass, although that showed signs of improving in the second half.
Rueda's mixed run continues
Reinaldo Rueda has endured a mixed run as Chile coach since taking over in January last year. There are few signs of that changing, which is perhaps worrying for Chile just months out from the Copa America. Rueda has overseen just four wins in 11 games.
Mexico take on Paraguay in a friendly on Tuesday, while Chile face the United States on the same day.