A general coherent control scenario to suppress or accelerate tunneling of quantum states decaying into a continuum is investigated. The method is based on deterministic, or stochastic, sequences of unitary pulses that affect the underlying interference phenomena responsible for quantum dynamics, without inducing decoherence, or collapsing the coherent evolution of the system. The influence of control sequences on the ensuing quantum dynamics is analyzed by using perturbation theory to first order in the control pulse fields and compared to dynamical decoupling protocols and to sequences of pulses that collapse the coherent evolution and induce quantum Zeno (QZE) or quantum anti-Zeno effects (AZE). The analysis reveals a subtle interplay between coherent and incoherent phenomena and demonstrates that dynamics analogous to the evolution due to QZE or AZE can be generated from stochastic sequences of unitary pulses when averaged over all possible realizations.