The Fenerbahce defender found himself free at a late Joao Moutinho set-piece at the Gillette Stadium in Foxborough and headed past a helpless Guillermo Ochoa.
With Cristiano Ronaldo still missing due to injury, Paulo Bento's men had lacked a creative spark until the late winner.
Portugal, who were held to a 0-0 draw by Greece last time out, face the Republic of Ireland on Tuesday before their World Cup campaign begins against Germany on June 16.
As expected, Portugal were without key trio Ronaldo, Pepe and Raul Meireles in Massachusetts.
Miguel Herrera started with Manchester United striker Javier Hernandez on the bench, while Rafael Marquez – who had been under an injury cloud – returned to the centre of defence.
Mexico pressed high up the pitch early on, but Portugal created an opportunity in the 14th minute as Vieirinha's strike was kept out by Jose de Jesus Corona.
Portugal forward Eder had the best chance of the first half when he was played through, but Mexico scrambled the danger away with Corona swatting the ball away.
Eduardo was forced into a save in the Portugal goal soon after as he tipped away a goal-bound cross from the left.
Eder looked the most likely to score in an uninspiring first half and he had another chance six minutes before the break, only to put Joao Pereira's cross wide.
Bento's men almost took the lead in the 50th minute.
A Nani corner eventually fell to Fabio Coentrao in the area, but the Real Madrid defender's low strike was kept out by substitute goalkeeper Guillermo Ochoa at his near post.
Just five minutes later, Mexico almost found an unlikely opener from range.
Hector Herrera played a square pass to Andres Guardado, whose powerful 25-yard drive went inches wide.
Hernandez needed just three minutes to have an impact off the bench as he almost set up Hector Herrera a minute after the hour-mark.
The striker's cross to the back post from the left found the Porto man, who took a neat touch before forcing Eduardo into a strong save from an angle.
The lively Hector Herrera tried his luck from range in the 68th minute, and Eduardo was up to the task once more to deny him.
Hernandez set up substitute Alan Pulido for a glorious chance in the 89th minute.
Played in behind, Hernandez unselfishly squared for Pulido, but Eduardo was quick off his line to smother at the forward's feet in a one-on-one.
But there was to be late drama as slack marking saw Alves rise in the area to head in Moutinho's free-kick from the right.
Mexico had their moments ahead of their first World Cup clash against Cameroon on June 13, while Portugal have one more friendly to improve their attack.
