Tom Heaton denied Sunderland a dramatic late winner as David Moyes' men were left mired in relegation trouble after spurning a series of chances against Burnley at the Stadium of Light.
Heaton saved well from Fabio Borini in the 87th minute while Billy Jones and Sebastian Larsson also missed fine opportunities as the Clarets recorded only their third away point of the season.
Burnley themselves will be disappointed not to go home with the points with Ashley Barnes prodding their best chance wide in the first period and substitute Sam Vokes coming close late on.
Barnes' miss was the only memorable moment of a grim first period, the ball spinning wide of keeper Jordan Pickford's right-hand post after Scott Arfield's low ball into the box beat the offside trap.