Fister (12-7) scattered four hits, worked around four walks and struck out four, tossing 63-of-112 pitches for strikes.
Phil Coke and Bruce Rondon combined for a scoreless eighth and Jose Veras recorded his 21st save as the AL Central-leading Tigers took the first of a three-game series against AL East counterparts Boston.
Red Sox starter John Lackey (8-12) was hung with the loss, surrendering three runs on seven hits over 7 1/3 innings.
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