Price (19-5) ran his strikeout total to 201 for the season while lowering his major league-best ERA to 2.56 with his fourth career complete game.
The left-hander allowed a pair of runs and didn't issue a walk as the surging Rays won their sixth straight. They came into the contest three games out of an American League wild card spot.
Jeff Keppinger went 2-for-4 with a three-run homer in the second inning that put Tampa Bay ahead to stay.
Clay Buchholz (11-7) was tagged for five runs (four earned) on eight hits over six full innings for the Red Sox.
Danny Valencia got Boston's only RBI.
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