Kevin Nolan gave the Magpies the lead with a 43rd-minute penalty before Kenwyne Jones equalised with a header midway through the second half. Defender James Perch headed into his own net with five minute remaining to give Stoke their second win of the season.
The win lifts Stoke out of the bottom three up to 14th, above Blackpool on goal difference.
For all their dominance, however, Newcastle also failed to create any real goal-scoring opportunities. Hatem Ben Arfa fired two free-kicks off target, while Joey Barton hit the wall with another, but on the whole the home side could not convert their possession into chances.
The Magpies finally took the lead just before half-time when Robert Huth inexplicably hauled down Andy Carroll in the area as Jose Enrique's cross floated harmlessly towards Thomas Sorensen, and Nolan calmly converted the spot-kick into the bottom corner for his third of the season. The goal meant that Stoke continued their run of trailing at half-time in every league match so far this season.
Jones was unfortunate to see his powerful header hit the foot of the near post, and Fuller could only pull his follow-up effort wide. Trinidad and Tobago striker Jones then had another solid headed effort crash back off the crossbar.
Jones finally converted a header at the third time of asking, but the goal came at a price. Fuller turned inside Jose Enrique with a neat turn wide on the right but landed awkwardly as the full-back fouled him. Fuller was replaced by Eidur Gudjohnsen just 20 minutes after coming on, and taken straight to hospital with a suspected dislocated shoulder.
However, Jones scored the leveller from the resulting free-kick, making no mistake from close range after Robert Huth headed the delivery back across goal for his fourth goal in as many games.
The introduction of Jonas Gutierrez added another dimension to Newcastle's play, and after Stoke equalised they upped the tempo. Carroll directed a volley form the Argentine winger's cross right at Sorensen.
However, Stoke were happy to soak up the pressure and hit Newcastle on the break, and they got their reward when Perch got in front of Huth at the near post to meet a Stoke corner, but could only head into his own net.
Newcastle laid siege to the Stoke goal during the six minutes of added time, but Nolan could only steer another good Gutierrez cross wide and Perch had his late effort blocked by Huth, consigning Chris Hughton's side to back-to-back home defeats.