Buchholz (7-0) allowed a run on five hits in his 10th start of the year and became the first Boston pitcher to open a campaign with seven consecutive victories since Josh Beckett did so in 2007.
David Ortiz doubled home two runs in the first inning and the Red Sox did not score again until the eighth.
Will Middlebrooks delivered a sacrifice fly in the eighth and Mike Napoli scored later in the inning on a passed ball. Daniel Nava had a two-run single in the ninth to give the Red Sox a 6-1 lead.
Paul Konerko hit a solo homer in the bottom of the ninth for Chicago, which had won the first two contests in the three-game series.