Bradley scored in the 20th and 60th minutes in the home win. Former Sweden international star Henrik Larsson scored twice for Helsingborg.
Danny Califf started and played the entire 90 minutes in Danish club AaB's surprise 2-2 tie at Italian club Sampdoria.
Brad Friedel was in goal for Blackburn Rovers in its 2-0 loss at Greek club Larissa that ended the English club's 15-game unbeaten streak.
For Oguchi Onyewu, the 2007-08 European campaign should be a short one. Belgian club Standard Liege dug itself a deep hole with a 3-0 loss at Russian club Zenit St. Petersburg.
None of the other Americans on UEFA Cup entrants played on Thursday: the injured Tim Howard (Everton), suspended Charlie Davies (Hammarby), Ramiro Corrales (Brann) and Johann Smith (Bolton Wanderers).