Vela put the visitors in front with a superb strike in the eighth minute and added a second goal in the 60th after Wesley Sneijder's sublime long-range equaliser.
Javier Hernandez dribbled past goalkeeper Tim Krul to add a third with a simple finish after 69 minutes before Daley Blind's deflected long-range shot five minutes later reduced the deficit.
Defeat heaps more pressure on Dutch coach Guus Hiddink, who has come under increased scrutiny, after Wednesday's defeat subjected them to a fourth loss in five matches since a third-placed finish at the World Cup.
Vela had not played for his country since March 2011 following a six month suspension for a breach of discipline by the Mexican Football Federation.
The Real Sociedad forward then repeatedly to return to the international fold following the punishment. The game was a rematch of the Netherlands' controversial 2-1 round of sixteen victory against Mexico in June.
Having led 1-0 with two minutes remaining in Brazil, Mexico lost 2-1 following late goals from Sneijder and Klaas-Jan Huntelaar, who converted a penalty won by an apparent Arjen Robben dive.
Hiddink made a host of changes on Wednesday from the team that succumbed to a surprise 2-0 Euro 2016 qualifying defeat against Iceland last month with Blind, Ibrahim Afellay, Sneijder and Robben the only players to retain their starting places.
Last week Hiddink, in his second spell as the Dutch coach, told a press conference he would quit if the Netherlands fail to beat Latvia in their Euro 2016 qualifying game on Sunday -- just three months after succeeding Louis van Gaal as coach.
The Netherlands are third in their Euro 2016 qualifying Group A, six points behind joint group leaders Iceland and the Czech Republic.
(Reporting by Geert Beckers, Editing by Tom Hayward)
