mesmerize

To exercise mesmerism on; to affect another person, such as to heal or soothe, through the use of animal magnetism.

Mesmer had about a hundred people whom he had instructed as magnetisers, some of whom belonged to the nobility, who also "mesmerised" people by making passes over the affected parts of the body.

To spellbind; to enthrall.

She mesmerized the audience with her tricks

Then he commenced to talk, really talk, and inside of two flaps of a herring’s fin he had me mesmerized, like Eben Holt’s boy at the town hall show. He talked about the ills of humanity, and the glories of health and Nature and service and land knows what all.