A pipe fitting socket for use with an axial driving device accepts a variety of angled fittings (e.g. tees, full elbows, slant elbows) snugly within a fitting cavity for torquing onto a fixed threaded end of pipe. Torquing of the fitting is accomplished by inserting a drive stud of the driving device into a drive aperture defining a rotational axis and torquing the driving device, thereby rotating the socket about the rotational axis, or through manually torquing a cylindrical portion of the socket. The socket offers superior efficiency and safety over conventional pipe wrenches by maximizing the effective range of movement available for a wrench used for angled fitting installation and/or removal, while virtually eliminating a wrench's loss of grip on the fitting.