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 the second set was more competitive, Bjorkman always held the upper hand and advanced to the net at every opportunity.
Roddick, the top seed, saved two match points in the ninth game before ninth-seeded Bjorkman served out for the match 6-4.
