After keeping out West Brom at The Hawthorns last month, Sean Dyche's side went on to frustrate Brighton at the AMEX Stadium.
Both sides had their chances, with Matt Lowton's cross deceiving Mat Ryan and striking the bar in the first half, but it was the Seagulls who crafted the better openings.
Nick Pope, who earned another England call this week, kept out Danny Welbeck on two occasions while Burnley's defence, which once again featured skipper Ben Mee, made countless blocks to keep their opponents out.
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Nick Pope, who earned another England call this week, kept out Danny Welbeck on two occasions while Burnley's defence, which once again featured skipper Ben Mee, made countless blocks to keep their opponents out.