A new method for the selective excitation of diatomic molecules in single vibrational states on excited electronic potentials by two-photon absorption is proposed. The method implies the use of two chirped strong pulse lasers detuned from the optical transition to an intermediate electronic state. We show under what scenarios the method is successful on the time-energy scale in which the pulses operate. They involved a long-time (nanosecond) weak-field regime and a short-time (picosecond) strong-field regime. The adiabatic representation in terms of energy levels or in terms of light-induced potentials is used to interpret the physical mechanism of the excitation. The efficiency and robustness of the scheme are demonstrated by the excitation of the ground vibrational state of the (1)Sigma(g)(4s) electronic potential of the Na-2 molecule.