Alexander gave the Red Bulls the lead when he slotted home after 16 minutes following some good work from Thierry Henry.
Henry was pulling the strings for his side and Fabian Espindola should have made it 2-0 when he was put through by the former Arsenal striker, but he could not apply the finish five minutes after the restart.
The New York outfit were made to pay for their profligacy late on when Jahn evened it up for the home side, before a handball inside the area gave Wondolowski the chance to grab the winner in injury time.
The striker's penalty was saved by Luis Robles, but officials had spotted some encroachment and ordered a retake.
Wondolowski made no mistake with his second spot kick to give the home side the points.