Last season’s beaten finalists took the lead with only 16 minutes gone when Jozy Altidore broke his 30-game scoring drought with a smart turn and low finish from the edge of the box which left Jack Butland rooted to the spot.
But Stoke responded before the break and were back on level terms when Oussama Assaidi cut in from the left flank and fed Muniesa, who burst into the box and then drilled a powerful low shot through Costel Pantilimon.
And the former Barcelona defender then hit the winner with 19 minutes to go when he seized possession on the left corner of the Sunderland penalty area and left Pantilimon grasping at thin air with his blistering drive.
Sunderland head coach Gus Poyet had indicated he would not make wholesale changes, while hinting he would select men who needed a game, but when the team-sheet arrived, it included the names of summer signings Pantilimon, Billy Jones, Sebastian Coates, Jordi Gomez and Will Buckley among seven new faces.
The Black Cats made a positive start with Altidore only just failing to get to Jones’ driven first-minute cross and Jack Rodwell firing inches over the top after latching on to Buckley’s cross.
However, if Sunderland were playing the more cohesive football, it was Stoke – themselves featuring six changes from the 2-2 Premier League draw at QPR – who were more accurate with Assaidi forcing a second-minute save from Pantilimon and Steven Nzonzi calling upon the Romanian once again nine minutes later.
But it was the home side who took the lead with 16 minutes gone when Jones helped Adam Johnson’s cross into the path of Altidore, who turned away from Robert Huth before drilling a low shot past the wrong-footed Butland.
As the game settled down, Stoke began to threaten on the break with Assaidi putting full-back Santiago Vergini under pressure, and when the equaliser arrived, it did so down his flank 14 minutes before the break.
Assaidi tricked his way past the Argentinian and fed supporting full-back Muniesa, who touched the ball outside John O’Shea before drilling it home off Pantilimon.
Butland did well to palm away Johnson’s curling free-kick three minutes later, but Assaidi really should have put the visitors ahead when he ran on to former Black Cat Phil Bardsley’s cross, only to slice his effort wide.
Nzonzi was fortunate not to see red after his scuffle with Rodwell, and the Potters midfielder might have taken full advantage with a strike which flew just wide on the stroke of half-time as the visitors finished strongly.
Neither side was able to gain any measure of control as the second half started in untidy fashion, and then descended into a drab affair fought out largely in the middle third.
That very nearly changed with 62 minutes gone when Rodwell picked out Gomez wide on the left and his cross was met by Buckley, whose guided volley looked to be going in until Butland threw out a hand to turn it away.
Jones was unable to make the most of a fine 67th-minute ball by Santiago Vergini and Buckley shot straight at Butland after being played in by Johnson seconds later, and they were made to pay with 18 minutes remaining.
Stoke were awarded a corner after Pantilimon tipped another Assaidi effort around the post and when the initial ball in was cleared, Muniesa muscled his way past Johnson before beating the keeper emphatically to snatch victory with substitute Victor Moses passing up an injury-time opportunity to extend their lead.