Lester battled with Brian Bannister in a tremendous duel that saw the teams combine for just seven hits.
J.D. Drew then struck out but Bates moved to third on a wild pitch and scored when Pedroia doubled on a 1-1 pitch from Bannister (6-7).
Lester (8-6) gave up four hits and struck out eight over eight innings.
Jonathan Papelbon worked a perfect ninth to record his 23rd save.
Kansas City put two runners on with no one out in the seventh, but Miguel Olivo flew into a double play and John Buck grounded out to end the inning.
2014: The Year in Music [PHOTOS]