A connector for tapered glass joints includes a first glass tubing section having a tapered sealing surface on an inner end surface thereof and threads on an outer surface of said end. A second glass tubing section has an end adapted to be telescoped into the end of said first tubing section, and a replaceable, resilient sealing sleeve is adapted to be sealingly engaged concentrically between the outer end surface of the second tubing section and the inner end surface of the first tubing section. A threaded cap is adapted to be threaded onto said threads of said first tubing section to secure the parts together and to force the sealing sleeve into tight sealing engagement with the respective tubing surfaces. A retaining ring may be carried by said second tubing section for cooperation with said cap to prevent relative axial displacement between said tubing sections when the cap is tightened, and also to enable said cap to be used as a jack against said ring to separate said tubing sections when the cap is unscrewed. In another form of the invention, a split cap and clamping ring are used for larger tubing.