Wiktionary
sleep off
vb. To get rid of (a pain, illness, condition) by sleeping.
WordNet
sleep off
v. get rid of by sleeping; "sleep off a hangover"
Usage examples of "sleep off".
The last prank had been to give the hens bread soaked in rum, which made them tipsy and scandalized all the other fowls, for the respectable old biddies went staggering about, pecking and clucking in the most maudlin manner, while the family were convulsed with laughter at their antics, till Daisy took pity on them and shut them up in the hen-house to sleep off their intoxication.