The loss, despite four hits by David Ortiz, left the Red Sox two games ahead of the New York Yankees with three to play.
The Yankees made up ground by beating the Tampa Bay Devil Rays 3-1.
Both Boston and New York already are assured of spots in the American League playoffs, which begin next week.
(Writing by Gene Cherry in Raleigh, North Carolina)
BOSTON (Reuters) - The Boston Red Sox failed to wrap up the American League East title when they lost to the Minnesota Twins 5-4 on Thursday.
