U.S. Open champion Roddick comfortably won his first match of the season on Tuesday, beating Russia's Nikolay Davydenko in straight sets, but struggled to find his rhythm against serve-and-volley specialist Bjorkman.
The Swede broke the 21-year-old American in the sixth game of the first set to go 4-2 up and then held serve to clinch it 6-3.
Although
Roddick, the top seed, saved two match points in the ninth game before ninth-seeded Bjorkman served out for the match 6-4.