The game was the first for the United States since its poor showing in last summer's World Cup, and also the first under interim coach Bob Bradley.
Dennis Sorensen gave Denmark a 1-0 lead in the 37th minute, heading in a pass from Simon Busk from the top of the U.S. box.
The United States tied the score just before halftime with a relatively weak penalty kick from Donovan that bounced into the net off the hands of goalkeeper Jesper Christiansen.
A pair of first-time international players did the rest of the U.S. scoring. Jonathan Bornstein converted a nice pass from Justin Mapp for the tie-breaking goal in the 59th minute, and Kenny Cooper broke away from a Denmark attack and rushed Christiansen all alone in the 82nd minute.