Laser-induced rotational wave packets of H_{2} and D_{2} molecules were experimentally measured in real time by using two sequential 25-fs laser pulses and a reaction microscope. By measuring the time-dependent yields of the above-threshold dissociation and the enhanced ionization of the molecule, we observed a few-femtosecond time delay between the two dissociation channels for both H_{2} and D_{2}. The delay was interpreted and reproduced by a classical model that considers enhanced ionization and thus additional interaction within the laser pulse. We demonstrate that by accurately measuring the phase of the rotational wave packet in hydrogen molecules we can resolve dissociation dynamics which is occurring within a fraction of a molecular rotation. Such a rotational clock is a general concept applicable to sequential fragmentation processes in other molecules.