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This match always looked likely to end goalless, with Middlesbrough struggling to score of late and Sean Dyche's Burnley determined to scrap their way to Premier League survival.
Robbie Brady went close with a couple of free kicks and Tom Heaton was called into action to protect his clean sheet, while Matthew Lowton twice made vital clearances to ensure the points were shared.
The draw means Middlesbrough are looking increasingly doomed, while Burnley -- promoted above Saturday's opponents as champions last season -- are close to securing their own survival.