Beckham's arrival should be a boost for injury-ravaged Milan, but the Rossoneri impressed with two goals and an assist from young Brazilian forward Alexandre Pato in the first 18 minutes.
Clarence Seedorf knocked home the rebound of Andrea Pirlo's free kick's off the post and Kaka scored from 20 yards for his second goal.
Beckham hopes to regain a spot on England's national team during the MLS offseason.
"I wouldn't take this opportunity if I didn't think that I could help the team and help the club," Beckham said.
Beckham is expected to play his first game for Milan on its post-Christmas trip to Dubai. Its next Serie A is at Roma on Jan. 11.
"He is in really great physical condition, I am told," said Milan vice president Adriano Galliani, "and I believe that after the period of preparation in Dubai, I believe he will be up to playing."
The loan deal expires March 9.
Milan is in third place in Serie A, nine points behind leader Inter Milan, which won, 2-1, at Siena on a pair of goals by Brazilian Maicon.
Second-place Juventus won, 3-1, at Atalanta on goals by Alessandro Del Piero, Nicola Legrottaglie and Amauri.