Buchholz yielded two runs on six hits, walking one and striking out four before leaving the game with neck tightness in the seventh inning. The right-hander may have been injured when he took a Howie Kendrick liner off his palm in the sixth and made an awkward throw to first, which was late.
With the performance, Buchholz's ERA rose slightly to 1.71, still the best in the major leagues.
David Ortiz smacked a two-run homer en route to three RBI while Dustin Pedroia added two run-scoring hits for the American League East-leading Red Sox, who bounced back from a 9-5 loss in Saturday's first game.
Angels starter C.J. Wilson (4-5) gave up four runs (three earned) on eight hits over five full frames.
Mike Trout and Mark Trumbo each drove in a run and Kendrick finished with three hits for Los Angeles.