win (one) over
To earn one's support. That candidate won me over with her performance in the debate.
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.
win over
Persuade, gain one's support, as in It won't be easy to win him over to our point of view. [Late 1800s]
win over
v. To succeed in gaining the favor or support of someone; prevail on someone: The politician spent a long time trying to win over the undecided voters. At first they didn't want to join us for dinner, but we finally won them over.