McClellan (3-0) gave up three hits and three walks with two strikeouts.
Daisuke Matsuzaka (0-2) went 5 2-3 innings, allowing two runs on three hits and two walks with four strikeouts.
The Cardinals sent 14 batters to the plate in the sixth inning and scored 10 runs, all with two outs. Albert Pujols delvered the big blow, a three-run double off Scott Atchison.
Matsuzaka got two quick outs before giving up a walk to Pujols and a run-scoring double to Matt Holliday. Left-hander Andrew Miller, vying for a spot in Boston's bullpen, came in to relieve, facing six batters without getting an out.