Benders decomposition is a technique to solve large-scale mixed-integer optimization problems by decomposing them into a pure-integer master problem and a continuous separation subproblem. To accelerate convergence, we propose Random Partial Benders Decomposition (RPBD), a decomposition method that randomly retains a subset of the continuous variables within the master problem. Unlike existing problem-specific approaches, RPBD is simple to implement and universally applicable. We present both computational and theoretical evidence to support its effectiveness. For example, in extensive numerical experiments on network design and facility location problems, we find that (i) RPBD accelerates the convergence of Benders decomposition for problems with and without relatively complete recourse; (ii) RPBD usually halves the optimality gap at termination compared with a standard Benders approach; (iii) a random retention strategy is just as effective as problem-specific approaches proposed in the literature.