IDIOMS

win over

(transitive, idiomatic) To persuade someone, gain someone's support, or make someone understand the truth or validity of something.

Example:   If the truth doesn't win him over, perhaps charm will.
2012 April 22, Sam Sheringham, “Liverpool 0-1 West Brom”[1], BBC Sport:
  Despite his ill-fated spell at Anfield, he received a warm reception from the same Liverpool fans he struggled to win over before being sacked midway through last season.