We study the impact of dust evolution in a protoplanetary disk around a T Tauri star on the disk chemical composition. For the first time we utilize a comprehensive model of dust evolution which includes growth, fragmentation and sedimentation. Specific attention is paid to the influence of grain evolution on the penetration of the UV field in the disk. A chemical model that includes a comprehensive set of gas phase and grain surface chemical reactions is used to simulate the chemical structure of the disk. The main effect of the grain evolution on the disk chemical composition comes from sedimentation, and, to a lesser degree, from the reduction of the total grain surface area. The net effect of grain growth is suppressed by the fragmentation process which maintains a population of small grains, dominating the total grain surface area. We consider three models of dust properties. In model GS both growth and sedimentation are taken into account. In models A5 and A4 all grains are assumed to have the same size (10(-5) cm and 10(-4) cm, respectively) with constant gas-to-dust mass ratio of 100. Like in previous studies, the three-layer pattern (midplane, molecular layer, hot atmosphere) in the disk chemical structure is preserved in all models, but shifted closer to the midplane in models with increased grain size (GS and A4). Unlike other similar studies, we find that in models GS and A4 column densities of most gas-phase species are enhanced by 1-3 orders of magnitude relative to those in a model with pristine dust (A5), while column densities of their surface counterparts are decreased. We show that column densities of certain species, like C2H, HC(2n+1)N (n=0-3), H2O and some other molecules, as well as the C2H2/HCN abundance ratio which are accessible with Herschel and ALMA can be used as observational tracers of early stages of the grain evolution process in protoplanetary disks.