Characterizing the ground-state properties of disordered systems, such as spin glasses and combinatorial optimization problems, is fundamental but computationally challenging. Finding exact ground states and counting their degeneracies are NP-hard and #P-hard, respectively, placing severe limits on exact algorithms. While tensor networks have emerged as a powerful paradigm for these tasks by leveraging massive hardware parallelization, their scalability is fundamentally bottlenecked by exponential memory growth. To overcome this, we introduce the Branch-and-Bound Tensor Network (BBTN) method. By integrating adaptive branch-and-bound search with efficient tropical tensor network contraction, BBTN sets new benchmarks for exact computation. It pushes the tractable frontier to previously unreachable scales, enabling exact ground-state counting for ±J spin glasses up to 65 × 65 and maximum independent set solving on King’s subgraphs up to 100 × 100, reducing runtimes required by state-of-the-art solvers from millions of years to hours. Furthermore, it consistently outperforms leading open-source integer-programming solvers and runs up to an order of magnitude faster than commercial solvers in rugged landscapes, establishing a versatile and scalable framework for solving hard problems in statistical physics and combinatorial optimization.