In a dour display, Sean Dyche & Co. bid farewell to top-flight games at Turf Moor for another year while the Potters reached their highest ever points total in the Premier League
After equalling their previous best haul of 50 last time out against Tottenham, Mark Hughes' side set a new record with their point in Lancashire.
Burnley dominated the opening exchanges but their struggles in front of goal continued, with Danny Ings denied on three occasions by Jack Butland as they failed to score for the fourth game in a row at Turf Moor in their final home match before returning to the Championship.
The visitors should have gone in ahead at the break with chances for Jonathan Walters and Mame Biram Diouf, with the latter also failing to convert another presentable chance after 55 minutes.
Hughes' attempts to win the game saw Peter Crouch and Peter Odemwingie brought on from the bench, but they were unable to find a way to all three points.
The draw ensures Stoke will finish the season in the top half, and keeps Sean Dyche's side off the bottom of the table on goal difference.
An unchanged Burnley side began brightly, with Ings - who is widely expected to leave the club in the close-season - immediately involved with a mazy run that lacked a quality finish.
Ings again threatened the Stoke defence with an effort on target as the hosts maintained their pressure, while the visitors, who were also unchanged, struggled to find their rhythm.
Butland, handed a third-successive start, was much the busier goalkeeper and had to be alert to deny Ings and David Jones in quick succession after 15 minutes, the 22-year-old making two excellent reflex saves to keep Burnley at bay.
With half an hour played, Stoke finally posed a threat on Tom Heaton's goal from a Charlie Adam set-piece, as Walters rose inside the penalty area but headed straight at the keeper.
Stoke finished the half strongly and would have gone into the break ahead had Walters and Diouf not blazed wide from promising positions.
After the restart, chances were at a premium at both ends with Diouf having the best opening shortly before the hour mark.
Burnley's defence twice failed to deal with an Adam cross, allowing the ball drop to the Senegal international, but Heaton made a fantastic save at his feet to keep the scores level.
Jason Shackell then made a timely interception to stop Diouf converting Marko Arnautovic's low cross.
Stoke's Steven N'Zonzi threatened to break the deadlock in the closing five minutes with a speculative long-range effort, but that skewed wide to ensure the game ended a stalemate.