The Orioles tried to rally in the bottom half of the 10th after a Mark Trumbo solo home run brought the score to 6-4, but Alex Colome closed out the rest of the inning.
The Rays jumped on the O's early on Wilson Ramos' first home run of the season, which also scored Souza, to go up, 2-0.
The O's relied solely on Rickard in the first half of Friday's game after he put Baltimore on the board in the third with an RBI double to left-center field to knock in Welington Castillo.