Spectrum prediction is a key enabler for the forthcoming coexistence paradigm where various Radio Access Technologies share overlapping radio spectrum, to substantially improve spectrum efficiency in 5G and beyond systems. Although this fundamental issue has received tremendous research attention, existing algorithms are designed for and validated against spectrum usage data in low time-frequency granularities, which causes inevitable errors when applied to spectrum prediction in realistic resolutions. Therefore, in this paper, we redesign three key components along the spectrum prediction pipeline to propose Effi-Ace, an efficient and accurate prediction for high-resolution spectrum tenancy. First, we obtain raw spectrum data in the same resolutions as scheduling, which reflects the actual dynamics of the subject to be predicted. We improve the Deep Q-Network (DQN) prediction algorithm with enhanced experience replay to reduce sample complexity, so that the proposed DQN is more efficient in terms of sample quantities. New prediction features are extracted from high-resolution measurement data to improve prediction accuracy. According to our detailed experiments, the proposed prediction algorithm substantially reduces sample complexity by 88. 9%, and the improvements in prediction accuracy are up to 14%, when compared with various state-of-the-art counterparts.