Wales were always likely to be up against it without the likes of Gareth Bale and Joe Ledley, and they struggled with the humidity and a lifeless pitch, failing to force a save from Mexico keeper Jesus Corona.
Monterrey striker De Nigris netted the opener in the 43rd minute as he headed home from inside the six-yard box and added a second with a chested finish a minute from time.
Mexico could have led inside 30 seconds as Carlos Salcido was able to pick out De Nigris far too easily with his long ball, but the striker fired wastefully wide.
Wales had another warning when a similar ploy picked out Tottenham's Dos Santos, but makeshift centre-half Chris Gunter recovered from his positional error to force the striker wide, with Brown making the save.
Both sides were being hindered by the slow playing surface but Mexico appeared to be adapting better as they continue to look the more threatening in attack.
Midfielder Andrade spurned a great opportunity when he was played in by Jesus Navala, blazing over from close range as Brown came out.
Wales' first effort on Corona's goal arrived after 25 minutes but Hal Robson-Kanu could not make a meaningful connection on Craig Bellamy's cross as his header glanced wide.
Steve Morison then failed to control Bellamy's intelligent cutback as Coleman's side finally showed an attacking threat.
But Mexico still looked the more likely to find an opening and Andrade, whose sharp movement from wide areas was causing Wales major problems, again fired over before Dos Santos shot just wide of the near post after another teasing run.
And Mexico got the lead their dominance deserved just two minutes before the break, as Meza's overlapping run allowed him to deliver a perfectly-judged cross that beat Gunter for De Nigris to nod home from inside the six-yard box.
The goal was a hammer blow to Wales, and Mexico started the second half intent on adding to their lead.
Meza forced Brown into a low save before the keeper made a brilliant stop from Dos Santos' point-blank header, while Hector Moreno came within inches of tapping home captain Francisco Rodriguez's header across the face of goal.
Coleman made a triple substitution on the hour as Sam Vokes, Simon Church and Sam Ricketts replaced Morison, Robson-Kanu and the injured Adam Matthews respectively.
And it almost paid dividends as Church linked well with Bellamy, with the Liverpool striker firing narrowly over Corona's crossbar.
Barrera volleyed well wide after he had been picked out by substitute Jorge Torres Nilo, while another substitute Angel Reyna was narrowly off target from the edge of the area.
With both sides making a raft of changes the game lost a lot of its shape during the final 15 minutes although Wales were still having to survive some anxious moments.
And De Nigris' sealed the win in the 89th minute as he intelligently chested home from Andrade's whipped delivery from the left.