Beat somebody at their own game
Definition 1 of 1
Pro Tip 1/3Competition Context
The phrase is often used in competitive scenarios, such as sports, business, or games. 
She trained hard and beat him at his own game on the tennis court.
Pro Tip 2/3Not Literal
It's usually not about actual games, but metaphorically overcoming someone in their specialty area. 
The underdog candidate beat the incumbent at his own game with a grassroots campaign.
Pro Tip 3/3Expertise Challenge
It implies that the person being beaten is usually the expert or perceived as better. 
The young chess prodigy finally managed to beat the grandmaster at his own game.