Implicit and explicit memory systems for motor skills compete with each other during and after motor practice. Primary motor cortex (M1) is known to be engaged during implicit motor learning, while dorsal premotor cortex (PMd) is critical for explicit learning. To elucidate the neural substrates underlying the interaction between implicit and explicit memory systems, adults underwent a randomized crossover experiment of anodal transcranial direct current stimulation (AtDCS) applied over M1, PMd or sham stimulation during implicit motor sequence (serial reaction time task, SRTT) practice. We hypothesized that M1-AtDCS during practice will enhance online performance and offline learning of the implicit motor sequence. In contrast, we also hypothesized that PMd-AtDCS will attenuate performance and retention of the implicit motor sequence. Implicit sequence performance was assessed at baseline, at the end of acquisition (EoA), and 24 h after practice (retention test, RET). M1-AtDCS during practice significantly improved practice performance and supported offline stabilization compared with Sham tDCS. Performance change from EoA to RET revealed that PMd-AtDCS during practice attenuated offline stabilization compared with M1-AtDCS and sham stimulation. The results support the role of M1 in implementing online performance gains and offline stabilization for implicit motor sequence learning. In contrast, enhancing the activity within explicit motor memory network nodes such as the PMd during practice may be detrimental to offline stabilization of the learned implicit motor sequence. These results support the notion of competition between implicit and explicit motor memory systems and identify underlying neural substrates that are engaged in this competition.