In this paper, we explore the stabilization problem of discrete-time Markov jump linear systems from a new perspective. We establish a novel learning-based framework that combines control theory and learning methods to design stabilizing feedback gains. Firstly, we reformulate the stabilization problems for discrete-time Markov jump linear systems into finite-time counterparts. Subsequently, leveraging techniques from the field of learning, we effectively and efficiently solve the finite-time stabilization problems. We systematically investigate two typical stabilization problems of discrete-time Markov jump linear systems within the proposed framework, namely the detector-based feedback stabilization and the static output feedback stabilization problems. Extensive simulation on various numerical examples demonstrates the advantages of our approach over several existing methods for discrete-time Markov jump linear systems.