The tubing connector system (100) provides a removable air-tight and water-tight sealing connection under vacuum conditions between an end portion (102) of a flexible tubing (104) and a tapping hole (108) on a main conduit (106). It includes a single screw-type clamp (120) having an adjustable tension mechanism (122) and a flexible metallic band (124) cooperating with the adjustable tension mechanism (122), a tube fitting (150), and a resilient gasket (180), to be interposed between an outer surface of the main conduit (106) and the inner side face of a flange (170) provided on the tube fitting (104), to seal a space immediately surrounding a tapping-hole engaging portion (162) on the tube fitting (104) when brought into cooperative engagement with the inner periphery of tapping hole (108). The sealing attachment can be created very quickly, even by an unexperienced operator, using parts that are relatively inexpensive and simple.