Isaac Brizuela's first-half goal was all that separated the teams at Estadio Akron in a feisty clash in Zapopan, Mexico.
Guadalajara – the 1962 champion – hit the front in the 26th minute thanks to Brizuela against the MLS visitor midweek.
The Red Bulls were caught out in an initial two-on-one situation before Rodolfo Pizarro rolled the ball through to Brizuela, who finished coolly past goalkeeper Luis Robles.
New York pushed numbers forward in the second half – Bradley Wright-Phillips and Florian Valot in the thick of the action.
However, the Red Bulls were unable to find a priceless away goal after Aurellin Collin saw red for a second yellow card with 17 minutes remaining as Wright-Phillips wasted a golden opportunity in a one-on-one situation moments later.