1
general::
Phrase(s): win someone over (to something)
to succeed in making someone favorable to something. • I hope I can win them all over to our side. • I won over the mayor to our side.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Persuade, gain one's support, as in It won't be easy to win him over to our point of view. [Late 1800s]
American Heritage Idioms