Paul Lambert's side dropped two points to Andy Carroll's late effort at West Ham on Monday, and they were once more unable to preserve an advantage on Sunday, though Ashley Barnes' scrappy strike came much earlier and the hosts were clinging on towards the end at the bet365 Stadium.
The Potters are now winless in 11 and four points off safety with three games to play after a display that promised much when Badou Ndiaye netted his first Premier League goal early on.
Stoke, once so dominant from set-pieces, allowed the threat on their goal to build through corners and free-kicks after the break and Barnes scrambled an equaliser into the net in the 62nd minute for his sixth strike in eight matches.
Burnley could not find a winner as their bid to overhaul sixth-placed Arsenal was dented, but they remain on course for the Europa League as Stoke face the increasing possibility of Championship football.
Up against England rival Jack Butland, Nick Pope was beaten after just 11 minutes. Mame Biram Diouf teed up Ndiaye to turn away from a defender and arrow a 20-yard strike into the bottom-right corner with the aid of a deflection.
Burnley's bustling front-line sought an immediate response as Barnes isolated Ryan Shawcross but could not quite get his right-footed finish to curl inside the far post.
An open game provided opportunities at both ends and Diouf flicked a header into Pope's hands, before Butland's first save of note repelled a swirling Johann Berg Gudmundsson free-kick.
A huge chance for Stoke to double their lead came and went before the break as Diouf missed his kick from Moritz Bauer's pinpoint centre.
4 - Badou Ndiaye is the fourth different Senegalese player to score for Stoke in the Premier League (after Diouf, Diao and Faye) - only Newcastle have had more (6). Lions. pic.twitter.com/Onf8zjI68k— OptaJoe (@OptaJoe) April 22, 2018
Some sloppy Stoke play handed Burnley the initiative following the restart and Butland was twice forced into action from headers at set-pieces, touching Jack Cork's looping effort over the top before parrying James Tarkowski's powerful nod to safety.
And another high ball into the box led to the equaliser. Butland again blocked from Tarkowski's header, but his attempt to scoop the ball clear instead ricocheted against Barnes and in.
Stephen Ireland almost pinched the points at the other end as he clipped the post, yet Stoke were grateful to Butland for another late stop from Gudmundsson - who was unfortunate to see another couple of shots go wide - and time is fast running out for Lambert's men as they prepare to travel to Liverpool next week.
Key Opta stats:
- Paul Lambert has now failed to win all of his five league meetings with Burnley as a manager (D3 L2). Only against Everton (eight) and Manchester United (seven) has he taken charge of more games in the top four tiers of English football without ever earning a victory.
- Burnley have lost only two of the last seven Premier League games in which they have conceded the first goal (W2 D3), having lost each of the seven beforehand.
-The Clarets have only kept one clean sheet in 15 league games in 2018; only Brighton (none) have kept fewer in the Premier League this calendar year so far.
- Ashley Barnes has scored six goals in his last eight league games, as many as his previous 44 combined.