Tā dòngzhīyǐqíng, xiǎozhīyǐlǐ, zhōngyú shuōfú le duìfāng.
He moved them with feeling and enlightened them with reason, and finally won them over.
Tips
usage
Almost always paired with 晓之以理 (to enlighten with reason) as a two-part formula: 动之以情,晓之以理 = "move them with feeling, reason with them logically." Core persuasion strategy in Chinese rhetoric.
grammar
Classical pattern 动 + 之 (object pronoun: "them") + 以 ("with; by") + 情 ("emotion"). Literally "move them by means of feeling."