Morrow held the Red Sox without a run, scattering four hits while striking out three and walking one.
The victory went to Brandon Lyon (3-0), who notched a pair of outs in the seventh to preserve a then-scoreless tie.
Boston's Jon Lester (9-12) absorbed the defeat, surrendering three runs on four hits over seven frames.
The Red Sox (66-81) were assured of their first sub-.500 season since 1997 with the loss.
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