From Longman Dictionary of Contemporary Englishhave somebody eating out of your handhave somebody eating out of your handCONTROLto have made someone very willing to believe you or do what you want He soon had the client eating out of his hand. → eat
Examples from the Corpus
have somebody eating out of your hand• He's brilliant in job interviews -- he always manages to get the panel eating out of his hand.• I introduced Mr Wilkinson to my mother, and within minutes she had him eating out of her hand.• In a second or two a man might have these boys eating out of his hand. 