Sheets, recalled from Class AAA Durham of the International League on Saturday, had three hits. The big blow came off starter Frank Castillo (5-11) with one out in the second, scoring Carl Crawford and Randy Winn to give the Devil Rays a 6-0 advantage.
Staked to a six-run lead, starter Joe Kennedy was unable to hang around and earn a decision. Jesus Colome (2-5) and Victor Zambrano each tossed three innings of scoreless relief, holding Boston hitless from the fifth through eighth innings.
Zambrano notched his second career save.
Casey Fossum, recalled earlier Wednesday, tossed a season-high seven innings as the Red Sox suffered their fourth loss in five games.