Win out
Definition 1 of 2
Pro Tip 1/3Emphasis on duration
Indicates a struggle or contest spanned a significant period before the winner emerged. 
The negotiations were tough, but common sense won out after weeks of discussion.
Pro Tip 2/3Metaphoric usage
Can be used to personify abstract concepts as contenders in a struggle where one prevails. 
In his heart, empathy won out over anger.
Pro Tip 3/3Positive connotation
Often suggests a desirable or favorable outcome in the end. 
After many failures, her determination to succeed won out.