Shaqiri impressed in flashes at Carrow Road, particularly in the first half, but Norwich piled on the pressure after the interval and were only denied victory by an outstanding display from Butland.
Mame Biram Diouf had headed Stoke into a first-half lead from a Shaqiri free-kick, but Russell Martin levelled for Norwich following a drinks break in the sweltering Norfolk temperatures.
After both Cameron Jerome and Wes Hoolahan spurned good chances, Butland produced saves out of the top drawer to thwart Nathan Redmond and then Graham Dorrans twice as Stoke held out for a point.
The Potters had won just once from the last 10 visits to Carrow Road, but they went into the match feeling confident having recovered from 2-0 down to draw at Tottenham last weekend, and with Shaqiri available.
They were in front after just nine minutes when Diouf got goalside of marker Alex Tettey to guide a left-wing free-kick from Shaqiri into the far corner with a fine diving header.
Norwich, who had an offer rejected for Stoke forward Jonathan Walters on Friday, looked for a quick response but lacked ideas in the final third.
With temperatures rising, referee Mike Dean allowed the players a brief drinks break at 25 minutes, and Norwich got themselves level just three minutes later.
Butland pulled off a brilliant reaction save to deny Martin at point-blank range. However, the ball was not cleared and when Redmond knocked it back into the penalty area, the Norwich skipper this time swept a low shot past the keeper and into the bottom corner for his second goal in as many games.
Stoke thought they had regained the lead when Ibrahim Afellay robbed Tettey following John Ruddy’s scuffed clearance and played in Diouf to slot home, but the forward was well offside.
Norwich full-back Robbie Brady, signed from relegated Hull, whipped a 25-yard free-kick over the wall and just wide.
The Canaries should have taken the lead at the start of the second half.
First, former Stoke forward Jerome stabbed the ball wide after being picked out by Jonny Howson in the penalty area. Brady then floated over another pin-point delivery, which was headed wide from six yards by Hoolahan.
Dorrans then charged into the right side of the penalty area, driving in a low shot which Butland pushed behind at full stretch.
On 62 minutes, Redmond got behind the Stoke defence, but his low shot across goal was tipped away by in-form Butland.
Another drinks break followed with 20 minutes left and Norwich then pressed for a late winner, but Butland saved Stoke again as he pushed away a fierce, low 20-yard effort from Dorrans.
From the corner, Jerome’s acrobatic effort at the far post deflected into the chest of the brave Stoke keeper.
In stoppage-time, substitute Bradley Johnson fired over from two yards after arriving to a free-kick at the back post, which just about summed up Norwich’s afternoon.