Crawford's game winning hit came against right-handed relief pitcher Jim Hoey, who entered the game with a 5.40 ERA and left with a 6.75 ERA. Meanwhile, Minnesota had a much better righty warmed up and sitting on the bench. Why didn't they use him? Because Matt Capps is the closer. And the role of closers is to save games.
Having suffered through multiple stretches of watching Boston put together a "closer by committee," I understand the comfort in knowing who is going to be pitching your team's last three outs, should they get ahead. But the 11th inning that is happening right now is a whole lot important than some future inning that may or may not occur. Their closer should have been in the game, giving their hitters a chance to get to the 12th inning.
Of course, I still think Crawford would have come through!