We present a novel content-driven memory pressure balancing and video memory power management scheme for parallel High Efficiency Video Coding (HEVC). The key is to leverage the application-specific knowledge to balance the (instant) access pressure on Scratchpad-based Video Memories (SVMs) for parallelized video processing. Our scheme accurately predicts the memory requirements of each processing core based on monitored memory usage and leverages this knowledge to perform a categorization of different video regions. Afterwards, it employs an adaptive policy for memory pressure balancing by rescheduling encoding of different video blocks based on their categories. This balancing also facilitates our scheme to perform efficient power-gating of unused parts of SVMs. Experimental results show that our scheme reduces the variations in the memory pressure by 37%-83% when compared to the traditional raster scan processing for 4-and 16-core parallelized HEVC encoder. Our content-driven power management saves 56% (on average) of SVM leakage energy.