Win around
Definition 1 of 1
Pro Tip 1/3Persuasive Effort
Shows effort to change someone's mind or gain their support through reasoning or appeal. 
She managed to win around her parents to her side after hours of discussion.
Pro Tip 2/3Positive Outcome
Implies achieving a successful result after convincing someone. 
Despite initial resistance, the marketing team was won around to the new strategy.
Pro Tip 3/3Change of Belief
Used when someone's belief or opinion is altered to align with yours. 
I finally won him around to believing that environmental conservation is crucial.