Burnley looked set for victory until Jon Harley fouled Richard Cresswell.
Kyle Lafferty put Burnley ahead after three minutes when former Stoke star James O'Connor set him up to fire low past Carlo Nash from 18 yards.
Burnley keeper Gabor Kiraly produced a string of outstanding saves either side of half-time to keep Stoke at bay until Lawrence's last-gasp reprieve.
Stoke manager Tony Pulis:
"We conceded an early goal and it would have been easy to crumble, but they showed tremendous character. I just cannot praise the players enough.
"I thought we deserved at least a point as we put them under lots of pressure."
Burnley boss Owen Coyle on the late penalty:
"A draw would have been a good result before kick-off, but we are desperately disappointed we haven't won.
"The boys defended manfully and I was pleased with the performance."
Stoke: Nash, Griffin, Riggott, Cort, Pugh, Lawrence, Diao (Parkin 84), Delap, Cresswell, Sidibe (Gallagher 70), Fuller.
Subs Not Used: Simonsen, Shawcross, Wilkinson.
Booked: Diao, Cresswell, Lawrence.
Goals: Lawrence 90 pen.
Burnley: Kiraly, Alexander, Carlisle, Varga, Harley, Elliott, James O'Connor, Randall (Mahon 63), Lafferty (Spicer 78), Blake, Akinbiyi (Cole 81).
Subs Not Used: Jensen, Unsworth.
Booked: Lafferty, Harley.
Goals: Lafferty 3.
Att: 18,432
Ref: Howard Webb (S Yorkshire).
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