City fielded a largely experimental side with youngsters Dedryck Boyata, Ben Mee, Andrew Tutte, Scott Kay and Alex Tchuimeni-Nimely named in the starting XI.
The hosts took advantage of the visitors' inexperience to jump into an early lead when Dane Richards outstripped Wayne Bridge before crossing for Macoumba Kandji to fire home.
Emmanuel Adebayor was named in the starting line-up and looked in good touch as he forced Bouna Coundoul into a decent save in the opening period.
City got back on level terms after 55 minutes when substitute Greg Cunningham's cross was converted by Jo.
But the Red Bulls sealed the win 20 minutes from time when the impressive Richards rifled home a long-range effort via the crossbar.
Red Bulls: Coundoul, Miller, Ream, Mendes, Hall, Stammler, Lindpere, Robinson, Richards, Henry, Kandji.
Man City: Hart (Taylor 46), Onuoha, Boyata (Lescott 63), Mee (Toure 63), Bridge (Bellamy 82), Tutte, Kay (Zabaleta 81), Ireland (Cunningham 46), Tchuimeni-Nimely, Jo (A. Johnson 63), Adebayor.
Source: PA
>> Terms & Conditions