Carry/win the day
Definition 1 of 2
Pro Tip 1/3Positive Outcome
Used when a person or idea overcomes challenges to succeed. 
Despite skeptics, her persistence carried the day.
Pro Tip 2/3Metaphoric Victory
It's often used metaphorically to describe non-physical victories. 
Her eloquence in the debate carried the day.
Pro Tip 3/3Dramatic Situations
Often found in narratives to detail a pivotal winning moment. 
The underdogs fought hard and ultimately carried the day.