Ultrafast state-selective manipulation of populations under the control of shaped picosecond infrared laser pulses is investigated by means of computer simulations within the reduced density matrix formalism beyond the Markov approximation for the HOD molecule coupled to an unobserved quasi-resonant environment. The laser-driven dissipative quantum dynamics in a classical electric field is simulated for discrete vibrational levels within a two-dimensional model of the HOD stretches in the electronic ground state. Efficient population transfer with the probability up to 80-90% is demonstrated on a picosecond time scale in the presence of the environmental degrees of freedom which reduce the lifetimes of vibrational bound states into a picosecond time domain.