snooze off

verb2

1. •
   To drift off; to fall asleep

   • But lately, he'd been tossing about all day, too exhausted to get proper sleep, and only snoozed off toward the last hour. — 1977
2. •
   To sleep off

   • Let us imagine that the stomach in question belongs to your uncle Embry, snoozing off his Christmas banquet on his bed — 1985