Wales international Connor Roberts had given the Clarets a deserved lead over Stoke City at Turf Moor.
But Vincent Kompany’s side suffered yet another body blow when conceding an equaliser late on.
Potters’ substitute Connor Taylor, on loan from Arsenal, inflicted the damage on this occasion as the Gunner powered a header past Arijanet Muric.
Burnley have now surrendered 10 points from winning positions already this term, with Blackpool, West Brom, Preston, Cardiff City and Stoke all coming from behind to claim a point.
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Potters’ substitute Connor Taylor, on loan from Arsenal, inflicted the damage on this occasion as the Gunner powered a header past Arijanet Muric.