Aitor Karanka's side looked to be on their way to all three points after Harlee Dean headed the visitors in front midway through the second-half.
But with just four minutes of normal time remaining Stoke substitute Nick Powell claimed a share of the spoils for his side with a lucky finish.
In a game which lacked real attacking quality, Blues defended well in numbers and limited the hosts to very few chances until conceding so close to the end.
Karanka elected to make just one change to the side that drew against Rotherham last time out with Jon Toral replacing Scott Hogan, who dropped to the bench.
Blues started brightly at the bet365 Stadium and got the ball into the Stoke area on several occasions without making it count.
With just over five minutes played, Ivan Sanchez shot from distance, but his effort flew several yards over the bar.
Blues were continuing to press, making it difficult for The Potters to make any real offensive progress.
But in a rare foray forward Stoke were not too far away after Fletcher curled an attempt just a yard wide of Neil Etheridge's upright.
As the half went on the hosts were beginning to gain more of a foothold in the game and Fletcher was inches away from firing his side ahead after his powerful free-kick struck the bar.
With Stoke in the ascendancy, Blues were being forced to defend much more deeply than they had earlier in the game.
A minute into stoppage time at the end of the half, Stoke were awarded a free-kick in a dangerous position to the right of the Blues area.
The ball was curled in towards the far post, where it was headed back across the front of the goal by Souttar towards his teammate Gregory. But Gregory, who was off balance, headed over from just a coule of yards.
Half-time: Stoke 0 Blues 0
Blues made an energetic start after the break, but it was Stoke that fashioned the first chance following a corner.
The ball was swung in where it was met by a firm Clucas header. With the ball heading towards the back of the net, Lukas Jutkiewicz deflected it behind with his head via the bar.
Just ahead of the hour mark, Blues had half a chance when Pedersen's lofted pass found Jutkiewicz inside the area, but the striker lashed his shot high and wide.
Then at the other end of the pitch, Harlee Dean was forced to turn a dangerous cross into his box behind for a corner.
With 62 on the clock, Blues made their first change of the afternoon with Dan Crowley replacing Toral.
And then on 65 Blues took the lead. Sanchez whipped in a neat corner from the right and Blues captain Dean made no mistake as he powered home a header.
As Stoke sought to find a way back into the contest potters boss Michel O'Neill made a double substitution with Tyrese Campbell and Nick Powell joining the action on 72. And for Blues, Marc Roberts replaced Bela as Karanka looked to shore up his defence.
With time running out Stoke were looking to up the ante and Fletcher should possibly have done better as he headed over from 10 yards.
But with less than five minutes of normal time remaining Stoke pulled the game level in somewhat fortuitous circumstances.
Campbell's cross from the right found Powell. Powell shot from close range, but the ball deflected off Dean and squirmed over the line with Etherington wrong-footed.
Stoke: Davies, Chester, Souttar, Fox, Smith, Mikel, Clucas, Oakley-Boothe (Powell, 72), Tymon (McClean, 81), Gregory (Campbell, 72), Fletcher.
Subs not used: Butland, Batth, Brown, Thompson.
Bookings: Chester (56), Fox (82), Clucas (85).
Goals: Powell (86).
Blues: Etheridge, Colin, Friend, Dean, Pedersen, Sunjic, Clayton, Toral (Crowley, 62), Bela (Roberts, 72), Sanchez, Jutkiewicz (Hogan, 87).
Subs not used: Prieto, Dacres-Cogley, Gardner, Boyd-Munce.
Bookings: Clayton (87).
Goals: Dean (65).
Referee: John Brooks.