Sunderland's turgid goalless draw against Burney on Saturday kept them in the FA Cup, though with an unwelcome replay in the midst of their desperate bid for Premier League survival.
David Moyes' side offered little threat beyond two first-half efforts from the improving Jack Rodwell, and would have lost had Burnley been sharper in front of goal.
Sam Vokes was denied by a fine early save when one-on-one with Sunderland goalkeeper Vito Mannone and James Tarkowski hit a post with a second-half header. Sunderland had brief bright spells but were the poorer side for long periods.
But this was emphatically a game to forget, except that the draw imposes a midweek trip to Burnley between crucial league games at home at Stoke City and away to West Brom.