Electrical fixtures, such as junction boxes or recessed luminaires, include mounting brackets that support the fixtures from structural members while fasteners, such as screws or nails, are driven through the mounting brackets, thereby facilitating mounting the fixtures. Each of the mounting brackets has a general U-shape that includes at least three generally planar sides. The top side is generally perpendicular to the other two sides, and the top side connects the other two sides and together. The three sides define (in cross-section) a structural member receiver opening. An inside dimension of the structural member receiver opening is such that bracket fits snugly around at least a portion of a commonly sized wood or metal structural member, such as a furring strip or joist, used in ceiling construction. In one embodiment, two of the sides of the structural member receiver opening define an acute dihedral angle to hood around the edge of a metal furring strip.