Two goals in four second half minutes saw Stoke City recover from being a goal behind at the break and ensure that Palace's first away game back in the top flight ended in defeat, despite a positive showing from Ian Holloway's men.
At half-time it looked as though the Eagles were going to claim their first victory of the season after taking the lead via a well-taken finish by Marouane Chamakh, but a quickfire double from Charlie Adam and Ryan Shawcross meant the Eagles left the Britannia Stadium empty-handed.
The game took a while to get going with the only early attempt being a speculative shot by Adam from 25 yards, but Palace had an early penalty shout when a great ball by debutant Jose Campana found Joel Ward in the box who was bundled into the back of by Matthew Etherington but referee Andre Marriner waved play on.
Peter Crouch's aerial threat was Stoke's main weapon in the first half and he went close with a header from a deep Etherington cross on 21 minutes but couldn't keep his attempt down.
However just after the half-hour mark Palace scored their first Premier League goal of the new campaign. A long ball forward by Damien Delaney bounced awkwardly for Shawcross and Chamakh pounced on the hesitation. He then dummied Robert Huth before firing low under Begovic to send the travelling Eagles fans into raptures.
The lead nearly didn't last a minute though when an Adam delivery found the head of Crouch, and the former England striker's header hurtled towards the top corner but the slightest of fingertips from Julian Speroni diverted it onto the bar and out of his net.
Having been millimeters away from conceding, Palace went just as close when Dean Moxey was found on the edge of the area and took aim and saw his grasscutter beat Begovic but flash wide of the far post, and Campana saw a free-kick from 25 yards miss the target by fractions.
With confidence growing, the last thing Holloway's side wanted was half-time and following the interval Stoke began much brighter and after a wayward strike from Steven N'Zonzi, Jonathan Walters hurtled towards goal before blazing over the crossbar.
But two goals in four minutes completely turned the game on its head as the hosts recovered to take the lead. On 57 minutes a cross into the Palace penalty area wasn't cleared effectively and Walters held the ball up before laying it into the path of Adam to coolly stroke the ball into the bottom corner.
And four minutes Shawcross put the ball into the same corner past Speroni when once again a throw-in wasn't cleared past the edge of the area, and the chance fell kindly the centre-half to put his side in front.
Now chasing the game, the Eagles nearly reclaimed parity when Moxey found Jason Puncheon in space on the right, and he cut inside before hitting a shot at Begovic which squirmed under his outstretched arm but didn't have enough pace to cross the goalline.
N'Zonzi nearly wrapped the game up with 15 minutes to go when he smashed a rocket of a shot towards goal but saw it cannon back off the post, and moments after appearing as a substitute Kevin Phillips dragged a shot wide after Jonny Williams blocked an attempted clearance.
Late on Dwight Gayle nearly scored a wondergoal when he volleyed a diagonal ball by Kagisho Dikgacoi towards goal but saw his blast curl wide of the target but Stoke held firm to clinch the victory.
Stoke City: Begovic; Cameron, Shawcross, Huth, Pieters; Walters, Nzonzi, Wilson, Adam (Whelan 74), Etherington (Pennant 70); Crouch (Jerome 86). Subs not used: Sorensen; Muniesa, Jones, Wilkinson.
Palace: Speroni, Ward, Delaney, Gabbidon, Moxey, Puncheon (Phillips 76), Campana (Garvan 65), Jedinak, Dikgacoi, Gayle, Chamakh (Williams 65). Subs not used: Alexander, Dobbie, Wilbraham, Ramage.