In this Letter, we report the discovery of a strong correlation between the variability of narrow absorption lines (NALs) and the ionizing continuum from a two-epoch spectral sample of 40 quasars containing 52 variable CIV {lambda}{lambda}1548, 1551 absorption doublets. According to the concordance index, this sample is classified into two subsamples. Subsample I shows an anti-correlation between the variations of absorption lines and the continuum, while Subsample II exhibits a positive correlation. These results imply that these variable CIV {lambda}{lambda}1548, 1551 absorption doublets are intrinsic to the corresponding quasars and that their variations are caused primarily by the fluctuations of the ionizing continuum. Based on our analysis, we propose that there might be two kinds of absorption gas: one that is very sensitive to the continuum variations, and another that is not. In addition, we suggest that in many cases the emergence or disappearance of NALs is caused by fluctuations of the ionizing continuum.