win (one's) heart
To gain the love, affection, or admiration of someone. Can also be structured as "win the heart of (someone)." She wasn't too impressed with me when I first met her, but I managed to win her heart by opening up to her about my aspirations as an artist. The rising star has already won the hearts of fans across the country, as her career continues its meteoric rise.
win someone's heart
and win the heart of someoneFig. to gain the affection of someone; to win the love of someone exclusively. I hope to win her heart and make her my bride.
win somebody’s ˈheart
make somebody love you: The children have won the old man’s heart.The actress who played Natasha won the hearts of the audience.