Abiotic stress during growth readily reduces cotton crop yield. The different survival tactics of plants include the activation of numerous stress response genes, such as BREVIS RADIX (BRX). In this study, the BRX gene family of upland cotton was identified and analyzed by bioinformatics method, three salt-tolerant and cold-resistant GhBRX genes were screened. The expression of GhBRX.1, GhBRX.2 and GhBRXL4.3 in upland cotton was silenced by virus-induced gene silencing (VIGS) technique. The physiological and biochemical indexes of plants and the expression of related stress-response genes were detected before and after gene silencing. The effects of GhBRX.1, GhBRX.2 and GhBRXL4.3 on salt and cold resistance of upland cotton were further verified. We discovered 12, 6, and 6 BRX genes in Gossypium hirsutum, Gossypium raimondii and Gossypium arboreum, respectively. Chromosomal localization indicated that the retention and loss of GhBRX genes on homologous chromosomes did not have a clear preference for the subgenomes. Collinearity analysis suggested that segmental duplications were the main force for BRX gene amplification. The upland cotton genes GhBRX.1, GhBRX.2 and GhBRXL4.3 are highly expressed in roots, and GhBRXL4.3 is also strongly expressed in the pistil. Transcriptome data and qRT‒PCR validation showed that abiotic stress strongly induced GhBRX.1, GhBRX.2 and GhBRXL4.3. Under salt stress and low-temperature stress conditions, the activities of superoxide dismutase (SOD), peroxidase (POD) and catalase (CAT) and the content of soluble sugar and chlorophyll decreased in GhBRX.1-, GhBRX.2- and GhBRXL4.3-silenced cotton plants compared with those in the control (TRV: 00). Moreover, GhBRX.1-, GhBRX.2- and GhBRXL4.3-silenced cotton plants exhibited greater malondialdehyde (MDA) levels than did the control plants. Moreover, the expression of stress marker genes (GhSOS1, GhSOS2, GhNHX1, GhCIPK6, GhBIN2, GhSnRK2.6, GhHDT4D, GhCBF1 and GhPP2C) decreased significantly in the three target genes of silenced plants following exposure to stress. These results imply that the GhBRX.1, GhBRX.2 and GhBRXL4.3 genes may be regulators of salt stress and low-temperature stress responses in upland cotton.