After struggling past Virginie Razzano in the previous round, Stosur looked back to her dominant best against Hampton, dictating the early exchanges with her trademark forehand as she reeled off the first four games.
The set soon followed and, despite an improved display from Hampton in the second, a solitary service break in the seventh game proved enough for Stosur to wrap up a 62 64 win.
Meeting her for a place in the final will be Chang Kai-Chen, who upset No.8 seed Laura Robson in a serve-dominated three-setter. Having split the opening two sets, the decider went with serve all the way to the tie-break.
With a maiden WTA semifinal touching distance away, Chang could have been forgiven for faltering. However, it was Robson whose nerves got the better of her, as she handed over a couple of early mini-breaks before double faulting on match point to slump to a 64 36 76(4) defeat.
Chang is not the only player breaking new ground in Osaka this week, with both semifinalists in the bottom half, Heather Watson and Misaki Doi, appearing at this stage of a WTA event for the first time.
Watson booked her spot with a hard-fought win over Pauline Parmentier. In a match littered with service breaks, and closer than the scoreline suggests, Watson kept her composure at the business end of both sets to eventually close it out, 75 63.
"I am so excited to have reached my first WTA singles semifinal," Watson, who is also in the doubles semifinals with Kimiko Date-Krumm. "This is my first year playing in Japan and I absolutely love it.
"Getting to play doubles with Kimiko is so cool too. She is so popular here and the crowd support is amazing. I hope I can continue things tomorrow. I know it will be a tough match in both singles and doubles."
Doi, who was the only Japanese player to make it beyond the first round, delighted the home crowds once more by overcoming a slow start to win 12 of the last 15 games in a 26 61 63 defeat of No.7 seed Chanelle Scheepers.