The friendly was played just hours after MLS and the players' union announced a new collective bargaining agreement to avert a strike that had threatened next week's opening of the U.S. league's season.
There was a sell-out 25,000 crowd on Saturday, even though Santos striker Robinho, who is on loan from English Premier League side Manchester City, did not play.
An official of the Brazilian club said Robinho did not travel to the United States for the match because he was suffering from a slight thigh strain.
New York midfielder Joel Lindpere rifled home a low shot from the edge of the area after a free-kick rebounded to him to score the first goal after just 11 minutes at the $220 million stadium in Harrison, New Jersey.
Defender Mike Petke scored the second in the 43rd minute, smashing home from close range while two minutes later, Dane Richards fired past Fabio Costa for the third.
Santos scored a consolation goal in the last minute of the match when Germano headed in a free-kick.
PURPOSE BUILT
The Red Bulls are hoping the new stadium will represent a turnaround in the club's fortunes. They had the worst record in MLS last season winning five of 30 league matches.
The move to a stadium custom-built for football, comes after the club, previously known as the New York/New Jersey MetroStars, played 14 seasons at Giants Stadium, the home of the National Football League's Giants and Jets.
The Red Bulls' average crowd of 11,000 were often lost in the cavernous stadium that holds over 80,000, although the club did attract a crowd of 66,237 two years ago when David Beckham played his first match in New York with the Los Angeles Galaxy.
Most of the 15 other clubs in the league, now play in football-specific stadia, after initially playing in American Football venues.
The new stadium has real, not artificial turf, and is designed like a European stadium. A translucent polycarbonate and aluminum roof structure means all seats are covered.
The stadium was paid for with the help of $80 million of public investment in land infrastructure improvements and cost about twice the price of other new U.S. soccer stadiums.
The Austrian energy drink company Red Bull spent more than $100 million to acquire the team from AEG Entertainment in 2006.
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