Zinnia elegans Jacq. is an ornamental plant, widely used in landscaping. Heavy-metal pollution in urban and rural areas is still increasing, which determines the actuality of studying plants’ reactions to pollutants. Zinnia was not sufficiently studied in this regard, so the aim of our research was to identify morphophysiological changes in this species under excess copper concentration in the soil. For this, we treated a growth substrate with 200 µM CuSO4 solution for 20 days. At the end of the treatment, several morphological, biochemical, and molecular genetic traits were evaluated: the root and the shoot size; the concentration of H2O2 and malondialdehyde (MDA), as indicators of stress; the amount of the phenolic compounds and lignin; and the level of the expression of genes, which encoded their biosynthesis. The Cu amount in the substrate and zinnia organs was quantified using atomic-absorption spectroscopy; hydrogen peroxide, MDA, and phenolic compounds were determined spectrophotometrically, while the amount of lignin was determined according to Klason. Real-time PCR was used for estimation of the gene-transcription level. Lignin in tissues was visualized by fluorescent microscopy. In experimental plants, Cu accumulation was higher in the root than in the stem. This caused an increase in stress markers and a decrease in the root and stem lengths. For the first time for zinnia, it was shown that for several genes—4-coumarate-CoA ligase (4CL), cinnamoyl alcohol dehydrogenase (CAD), and class III peroxidase (PRX)—the level of expression increased under copper treatment. The rise of the transcripts’ amount of these genes was accompanied by a thickening and lignification of the cell walls in the metaxylem vessels. Thus, the adaptation of zinnia to the excess Cu in the growth medium was associated with the metabolic changes in the phenylpropanoid pathway. As a result, the lignification increased in the root, which led to the accumulation of Cu in this organ and limited its translocation through the xylem to the stem, which provided plant growth.