How do two-phase commits prevent last-second failure?
No, they are not instructed to roll back because in the original poster's scenario, some of the nodes have already committed. What happens is when the crashed node becomes available, the transaction coordinator tells it to commit again.
Because the node responded positively in the "prepare" phase, it is required to be able to "commit", even when it comes back from a crash.
Summarizing everyone's answers:
One cannot use normal databases with distributed transactions. The database must explicitly support a transaction coordinator.
The nodes are not instructed to roll back because some of the nodes have already committed. What happens is that when the crashed node comes back, the transaction coordinator tells it to finish the commit.