Measuring a quantum system can reveal information while disturbing its state. Consequently, the probabilities of obtaining desired outcomes in individual measurements constrain the probability of obtaining them in sequence. This interplay arises naturally in mistrustful quantum cryptography, where a dishonest participant may perform sequential measurements to extract more information than the protocol allows. We develop consecutive measurement theorems (CMTs) to quantify this constraint, relating the average success probability of a single measurement to that of an ordered pair of distinct measurements. For measurements on a common state, we derive the optimal lower bound on consecutive-measurement success as a function of single-measurement success and provide matching constructions over the entire parameter range. We also establish the first robust CMTs for measurements on different but nearby states, with closeness quantified by fidelity or trace distance. We use these results to strengthen sum-binding guarantees for relativistic bit commitment and soundness bounds for relativistic zero-knowledge proofs, and to obtain improved no-go results for quantum oblivious transfer and quantum private query. Our results establish CMTs as a versatile tool for translating consecutive-measurement constraints into concrete cryptographic bounds and suggest applications in other quantum-information settings.