Aldo de Nigris also scored as Mexico went three goals up in the first half against an inexperienced New Zealand defense, then made wholesale changes to its lineup for the second half.
This was Mexico's last game before the Gold Cup, where it will play in Group A against Costa Rica, Cuba and El Salvador. The team starts with El Salvador on Sunday and Manchester United forward Javier Hernandez is expected to be with the squad.
Hernandez missed the game against New Zealand, still recovering after playing in last weekend's European Champions League final.
Dos Santos, who spent the second half of the just-completed European season on loan from Tottenham at Racing Santander, put Mexico on the board first when he scored off a rebound in the 23rd minute. Carlos Salcido took a shot that bounced off the hands of New Zealand keeper Glen Moss and straight to the foot of dos Santos, who drilled the ball into the net.
Just 7 minutes later, dos Santos scored again by controlling a deflected ball in the box, rounding Moss and all but walking it into the net.
In the 43rd minute, de Nigris - having earlier had a goal ruled out for offside and having two close-range shots saved - finally got on the score sheet when he tapped in a pass from Andres Guardado.
Goalkeeper Guillermo Ochoa had an easy evening for Mexico, making only two saves for the game.