A topical composition includes a cannabinoid, a terpenoid, and a skin penetration system that includes dimethyl sulfoxide (DMSO) and at least one compatibilizer. The composition may be in the form of an emulsion that further contains water and at least one fatty component. The composition can be used to reduce or eliminate pain by topical application to an affected region of the body. The composition provides localized pain relief by providing a focused quantity of cannabinoid in the region of the pain instead of distributing the cannabinoid systemically and/or delivering it to the brain or central nervous system.