Elaeis guineensis is a significant source of vegetable oil, yet it does not thrive in dry conditions. Thus, it is essential to understand the molecular response to drought in multiple oil palm tissues. Here, we analysed publicly available transcriptomic data from the leaves and roots of oil palms following drought. We identified ~5000 genes with significant gene expression changes, further clustered based on their expression patterns into 12 groups. The gene clusters showed distinct expression patterns in the two tissues examined, highlighting the different biological mechanisms. The involvement of the phytohormone abscisic acid in drought is implicated in both tissues by the differential expression of the activating transcription factor (TF) families homodomain-leucine zipper (HD-ZIP), ethylene response element binding factors (ERF) and no apical meristem (NAM), Arabidopsis thaliana activating factor (ATAF) and cup-shaped cotyledon (CUC) (NAC). Gene clusters uniquely upregulated in leaves are enriched for TF family DNA binding one zinc finger (Dof) and lateral organ boundaries domain (LBD), which regulate hormone homeostasis and stomatal closure. Photosynthetic-related genes are downregulated in leaves, hypothesised to reduce photosynthesis activity, whereas heat shock proteins are enriched in upregulated genes found in roots. Finally, we assembled ribonucleic acid (RNA) sequencing reads to discover ~6200 novel genes whose expression are sensitive to drought. Our results expand the knowledge of molecular response following drought and demonstrate how identifying gene clusters can help to form hypotheses of molecular mechanisms.