Intracellular vesicular transport along cytoskeletal filaments ensures targeted cargo delivery. Such transport is rarely unidirectional but rather bidirectional, with frequent directional reversals owing to the simultaneous presence of opposite-polarity motors. So far, it has been unclear whether such complex motility pattern results from the sole mechanical interplay between opposite-polarity motors or requires regulators. Here, we demonstrate that a minimal system, comprising purified Dynein-Dynactin-BICD2 (DDB) and kinesin-3 (KIF16B) attached to large unilamellar vesicles, faithfully reproduces in vivo cargo motility, including runs, pauses, and reversals. Remarkably, opposing motors do not affect vesicle velocity during runs. Our computational model reveals that the engagement of a small number of motors is pivotal for transitioning between runs and pauses. Taken together, our results suggest that motors bound to vesicular cargo transiently engage in a tug-of-war during pauses. Subsequently, stochastic motor attachment and detachment events can lead to directional reversals without the need for regulators.