A nucleosome is composed of intrinsically disordered histone tails and a structured nucleosome core surrounded by DNA. A variety of modifiable residues on the intrinsically disordered histone tails have been identified in the last decade. Mapping of the functional residues on the structured nucleosome core surface was recently initiated by global analysis of a comprehensive histone point mutant library (histone-GLibrary). It stands to reason that a functional relationship exists between modifiable residues on the intrinsically disordered histone tails and functional residues on the structured nucleosome core; however, this matter has been poorly explored. During transcription elongation, trimethylation of histone H3 at lysine 36 (H3-K36me3) is mediated by histone methyltransferase Set2, which binds to RNA polymerase II. Here, we used a histone-GLibrary that encompasses the nucleosomal DNA entry/exit site to show that six residues (H2A-G107, H2A-I112, H2A-L117, H3-T45, H3-R49 and H3-R52) form a surface on the structured nucleosome core and regulate H3-K36me3. Trimethylation at H3-K4 introduced by histone methyltransferase Set1 was not affected by the mutation of any of the six residues. Chromatin immunoprecipitation analysis showed that most of these residues are critical for the chromatin association of RNA polymerase II and Set2, suggesting that these components regulate H3-K36me3 through functional interactions with the structured nucleosome core surface.