This phrase suggests a significant power imbalance, where one person has a great deal of control over someone else. She had her opponent in the palm of her hand throughout the debate.
Pro Tip 2/3
Captivated Audience
Often used to indicate rapt attention or fascination, as when someone captivates an audience completely. With his storytelling, the grandfather had the children in the palm of his hand.
Pro Tip 3/3
Emotional Influence
The phrase can imply that the person is being influenced emotionally, not just logically or by authority. With just a few words, she had him in the palm of her hand, ready to help her.