I think we are led to believe it was Luca Brasi's doing. Bribing whoever needed be. Without waking up Woltz would nearly be impossible. It's a great scene but very far fetched. Maybe he had his drink spiked to put him deep into sleep.

I'm quite surprised your initial question hasn't been answered. It's a good topic.

My vote is for Luca Brasi. Definatelly the most interesting character in the book. Now during the book we are forced to read about his evilness, the baby and the Capone's men incidents. But somehow because of his loyalty to Don Corleone we accept him because we like Vito Corleone for all the reasons Machiavelli wrote. It's just a pity the film made him out to be a bumbling idiot.