Klinsmann's team had beaten Cuba 2-0 in a friendly four days ago in Havana, with Green scoring one of the goals.
He notched another goal in the 27th minute, but the Americans were uninspiring after the break and New Zealand deserved their equaliser in the 72nd minute.
The 19-year-old Patterson, who plays for Ipswich Town in the English second tier, poked home a loose ball in the box following a corner, the ball taking a deflection and squirming between the legs of U.S. keeper David Bingham.
New Zealand had the U.S. on the rack for much of the final 20 minutes, but could not find a winner, before the home team created a few late chances.
The U.S. begin their final World Cup qualifying phase, known as the Hexagonal, against Mexico in Columbus, Ohio, on Nov 11.
New Zealand, meanwhile, are expected to win the Oceania confederation, before a playoff against the fifth-ranked team from South America for a berth in Russia 2018.
The All Whites were edged 2-1 by Mexico in a friendly in Nashville on Saturday.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Greg Stutchbury)
