A mathematical model of the suspension flow forced by colored random disturbances is considered. We focus on the parameter zone adjacent to the Andronov–Hopf bifurcation separating stable equilibrium and self-oscillatory modes. A phenomenon of stochastic excitement with colored-noise-induced generation of spiking oscillations in the equilibrium zone is investigated. We show how colored noise shifts boundaries of oscillation modes, and study dependence of this shift on the correlation time parameter. Zones of the stochastic resonance are revealed and parametrically described in terms of probability of excitement.