The feasibility of achieving coherent control of tunnelling dynamics, associated with electronic excitations in functionalized semiconductor nanostructures, is investigated. The coherent control scenario is based on the application of frequent stochastic unitary pulses, affecting the interference phenomena between electronic wave-packet components and consequently the overall electronic tunnelling dynamics without collapsing the coherent quantum evolution of the system. It is shown that tunnelling can be inhibited and eventually halted by sufficiently frequent pulse fields that exchange energy with the system but do not affect the potential energy tunnelling barriers. Further, the proposed stochastic quantum-control scenario is demonstrated more generally as applied to an archetype model, a particle tunnelling in a quartic double-well potential.