The ^{12}C(^{18}O,^{16}O)^{14}C and ^{12,13}C(^{18}O,^{17}O)^{13,14}C reactions are studied at 84 MeV. Mass distributions and energy spectra of the ejectiles are measured, indicating the selectivity of these reactions to populate two- and one-neutron configurations in the states of the residual nucleus, respectively. The measured absolute cross-section angular distributions are analyzed by exact finite range coupled reaction channel calculations based on a parameter free double-folding optical potential. The form factors for the (^{18}O,^{16}O) reaction are extracted within an extreme cluster and independent particles scheme with shell-model-derived coupling strengths. The results show that the measured cross sections are accurately described for the first time without the need for any arbitrary scaling factor. The (^{18}O,^{16}O) reaction is thus found to be a powerful tool for quantitative spectroscopic studies of pair configurations in nuclear states.