Sunderland and Burnley will contest a third-round replay after playing out a dire goalless draw in front of under 18,000 fans at the Stadium of Light.
The Clarets, who included Joey Barton for the first time since he re-joined the club, went close when Sam Vokes was put clear but saw his shot saved.
The visitors had the better chances but keeper Nick Hope did well to tip a Jack Rodwell shot over the bar.
And Burnley almost won it when James Tarkowski's header struck the post.
More to follow.
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Everton are without Senegal midfielder Idrissa Gueye for Saturday's FA Cup third-round tie against Leicester as he has left for the Africa Cup of Nations.