1 general:: Fall into a light sleep, as in Watching the ballet always made her doze off. [Mid-1800s]
American Heritage Idioms
2 general:: Phrase(s): doze off (to sleep) to slip away into sleep. • I dozed off to sleep during the second act of the opera. • I was so comfortable that I just dozed off.
McGrawhill's American Idioms And Phrasal Verbs