Marouane Chamakh gave the visitors the lead but Mark Hughes' side manage to turn the match around in the second half to leave the Eagles pointless after two games
Marouane Chamakh had put Palace ahead in his first start for the club, capitalizing on Shawcross' mistake to fire home, before Charlie Adam equalized with a smart finish.
But it was Shawcross who had the last word, finishing from close-range after Palace had failed to clear from a Stoke corner.
Midfielders Brek Shea, Wilson Palacios and Jamie Ness all missed out through injury for the home side, but Hughes handed a home debut to Erik Pieters, a close-season buy from PSV Eindhoven.
Palace, meanwhile, gave a debut to Southampton loanee Jason Puncheon, while former Arsenal striker Chamakh made his first start for the club after coming off the bench last week against Tottenham.
Hughes' appointment for Stoke came with the promise of an improved playing style and, although Peter Crouch's height was still utilized, they generally looked to pass the ball short, as opposed to the direct style favored by Tony Pulis.
The game's first chance fell to Adam, but the Scotland international's drive from outside the area went straight at Julian Speroni.
Palace threatened after 16 minutes when Dwight Gayle seized onto a loose ball on the left wing and raced into the Stoke area, but his left-footed shot was saved by Asmir Begovic.
Crouch almost opened the scoring for Stoke when he met Matthew Etherington's dinked left-wing cross at the back post, but his header flew over.
And after 32 minutes the hosts were made to pay as Palace scored the opener - Ryan Shawcross failing to deal with a long ball before being out muscled by Chamakh, who finished clinically on his right foot from just inside the area.
Stoke tried to respond immediately through Crouch, but his header from Adam's cross was tipped onto the underside of the crossbar by Speroni, before left-back Dean Moxey nearly put Palace two up with a left-footed drive that flashed wide before the break.
The hosts, though, started the brighter at the start of the second half and their equalizer arrived when Palace failed to deal with a left-wing cross and Crouch then Jonathan Walters worked the ball wide to Adam, who finished well.
And just four minutes later, Stoke was ahead. Robert Huth did well to charge down a Palace clearance and the ball broke to Shawcross, who slotted home from six yards out.
At the other end, Begovic came to Stoke's rescue with a brilliant save down to his left from Puncheon's drilled effort.
As the visitors pushed for a late equalizer, Gayle struck an audacious volley from wide on the right of the area, but it arrowed past the post and the hosts held on for a first win of the season.