The British number two was repeatedly treated for a shoulder issue as she went down 7-5 6-3 in one hour 49 minutes after failing to follow-up the dramatic, late night, three-set win over eighth seed Petra Kvitova on Thursday.
Stephens proved to be made of sterner stuff as she came through to deny Robson a second successive fourth-round grand slam appearance following her memorable run at the US Open.
Stephens made a blistering start, blasting winners from all angles to make Robson look lethargic.
In her defence, the 18-year-old's uncomfortable movement may have been attributed to a problem in the shoulder area which became apparent after the fifth game when she called for a medical timeout.
At that point Stephens had not made an unforced error and was flying even though her progress, having broken twice, had just been checked as Robson claimed one back.
The delay clearly stalled the American's momentum as Robson mounted a comeback, breaking again to get it back on serve.
Stephens` attacking game had deserted her as she became content to push the ball down the middle of the court and wait for her opponent to make an error.
It almost worked as she brought up two set points with Robson serving at 4-5.
But the Briton's tenacity came to the fore as she saved the first with a big cross-court forehand and the second when Stephens could only frame a forehand out of court.
The 29th seed threatened again two games later and this time Robson could not find an escape route as she drifted a backhand wide, although she may claim to have been put off by someone in the crowd loudly declaring Stephens' previous shot out.
Robson had a third spell of treatment at the end of a set in which she coughed up 29 unforced errors to just six winners.
She remained the aggressor at the start of the second but Stephens was proving deceptively canny, mixing blazing groundstrokes with periods of passive play.
And the change in pace appeared to unsettle Robson as she failed to find any kind of rhythm.
It was to prove damaging as Stephens made her move in game four.
Having staved off three break points, Robson could not repeat the feat a fourth time as Stephens lured her towards the net and then ripped an unreturnable drive at the feet.
She advanced without alarm to 5-3 before some late nerves almost gave Robson a way back.
Serving for the match, Stephens had to stave off two break points before setting up her first chance to win the match.
She fluffed her lines, dumping a routine backhand volley into the net but made no mistake second time round when Robson thrashed a wild forehand wide - her 47th unforced error of the match.
Stephens, 19, who also beat Robson in Hobart last week, will play either 42-year-old Kimiko Date-Krumm or Bojana Jovanovski next.