It was a disastrous start to the game for Steve McClaren's side as Jamaal Lascelles brought down Gonzalo Bergessio inside the box, and it was the Atlas forward who stepped up to beat Tim Krul with a calm penalty.
The lead was doubled just six minutes later when a high ball was sent forward to Bergessio, who left Krul helpless with a stunning volley.
Bergessio came agonisingly close to completing a hat-trick midway through the first half, but his effort rebounded off the crossbar as the Newcastle defence continued to look vulnerable.
Despite conceding two early goals, Newcastle regularly threatened at the other end of the pitch and they were rewarded for a long spell of pressure when Papiss Cisse sprinted into space and found Moussa Sissoko, who slotted home from a tight angle to reduce the deficit just before the break.
The Magpies came agonisingly close to getting back on level terms with the Mexican side early in the second half, but Siem de Jong could only drag his shot wide of the post.
Atlas continued to invite pressure from McClaren's side, and Newcastle created another chance when Yoan Gouffran drifted into space before sending an effort over the crossbar.
Newcastle made six changes late on, and despite an impressive cameo from substitute Rolando Aarons, they were unable to find an equaliser in the closing stages as Atlas held on for the win.