Wild relatives of wheat are an outstanding source of resistance to both abiotic and biotic stresses. In the present study, we evaluated the activity of four antioxidant enzymes—superoxide dismutase (SOD), catalase (CAT), ascorbate peroxidase (APX) and guaiacol peroxidase (GPX)—along with photosynthetic pigments and shoot biomass in 12 Aegilops–Triticum accessions with different genomic constitutions and two tolerant and sensitive control varieties under well-watered (WW; 90% FC), moderate (MS; 50% FC) and severe (SS; 25% FC) water stress treatments. The analysis of variance for measured traits indicated highly significant effects of the water stress treatments, accessions, and their interactions. The 12 domesticated and wild relatives of wheat exhibited more variability and greater activity in the expression of antioxidative enzymes than cultivated wheats. While domesticated forms of wheat, T. aestivum (AABBDD) and T. durum (AABB) seem to have a functionally active antioxidant mechanism, other accessions with alien genomes—Ae. umbellulata (UU), Ae. crassa (MMDD), Ae. caudata (CC), Ae. cylindrica (DDCC) and T. boeoticum (AbAb)—respond to water stress by increasing enzymatic antioxidants as the dominant mechanism that contributes to the retention of oxidative balance in the cell. Furthermore, abovementioned accessions with alien genomes had higher photosynthetic pigment contents (chlorophyll a, chlorophyll b, total chlorophyll, and carotenoid) under water stress than well-watered conditions. Hence, these accessions could be used in future breeding programs to combine beneficial stress-adaptive characters of alien genomes into synthetic hexaploid wheat varieties in the field, even at limited water supply.