This article considers a subspace guarding game in high-dimensional space which consists of a play subspace and a target subspace. Two faster defenders as a team cooperate to protect the target subspace by capturing an attacker which strives to enter the target subspace from the play subspace without being captured. A closed-form solution is provided from the perspectives of kind and degree. Contributions of the work include the use of the attack subspace (AS) method to construct the barrier, by which the game winner can be perfectly predicted before the game starts. In addition to this inclusion, with the priori information about the game result, a critical payoff function is designed when the defenders can win the game. Then, the optimal strategy for each player is explicitly reformulated as a saddle-point equilibrium. Finally, we apply these theoretical results to two half-space and half-plane guarding games in 3-D space and 2-D plane, respectively. Since the entire achieved developments are analytical, they require a little memory without the computational burden and allow for real-time updates, beyond the capacity of the traditional Hamilton-Jacobi-Isaacs method. It is worth noting that this is the first time in the current work to consider the target guarding games for arbitrary high-dimensional space and in a fully analytical form.