Khudobin, third-year pro, turned aside 26 shots en route to his first shutout since Jan. 16, 2011, when he was a member of the Minnesota Wild, improving to 7-3-0 on the season.
Boston holds the third seed in the Eastern Conference.
Ryan Miller made 29 saves for Buffalo, which dropped its fourth straight.
Wisconsin business offering 'therapeutic cuddling' forced to close
Workers accuse National Zoo of animal mismanagement