Crede led off the sixth with his ninth homer of the season to give Chicago a 3-1 lead. Konerko's blast, his sixth, opened the eighth inning and extended the White Sox' advantage to 5-1.
Edwin Jackson (3-4) gave up four runs on 10 hits in six innings to suffer the loss.
Tampa Bay had not lost a series opener since May 2.
Earlier in the day, Tampa Bay put pitcher Troy Percival on the 15-day disabled list with a left hamstring strain.