Understanding protein-DNA interactions, specifically transcription factor (TF) and transcription factor binding site (TFBS) bindings, is crucial in deciphering gene regulation. The recent associated TF-TFBS pattern discovery combines one-sided motif discovery on both the TF and the TFBS sides. Using sequences only, it identifies the short protein-DNA binding cores available only in high-resolution 3D structures. The discovered patterns lead to promising subtype and disease analysis applications. While the related studies use either association rule mining or existing TFBS annotations, none has proposed any formal unified (both-sided) model to prioritize the top verifiable associated patterns. We propose the unified scores and develop an effective pipeline for associated TF-TFBS pattern discovery. Our stringent instance-level evaluations show that the patterns with the top unified scores match with the binding cores in 3D structures considerably better than the previous works, where up to 90 percent of the top 20 scored patterns are verified. We also introduce extended verification from literature surveys, where the high unified scores correspond to even higher verification percentage. The top scored patterns are confirmed to match the known WRKY binding cores with no available 3D structures and agree well with the top binding affinities of in vivo experiments.