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.
1. Nick Pope 7
Commanded his area with authority, his handling was 'as safe as houses', and he was as vocal as ever. Made two big stops to deny Welbeck in the first half, saving with his legs and then smothering the ball at the striker's feet later on.
2. Matt Lowton 5
His poor pass left Pope completely exposed as Welbeck raced clear in the first half and was often troubled by the runs of Lallana and Maupay in behind. Got forward well, couldn't dig out a killer cross, though struck the woodwork in the first half.
3. James Tarkowski 7
Dominant in the air, both when challenging for the ball and getting on the end of countless Brighton crosses into the box. Read the game very well and got into positions to clear the danger time and time again.
4. Ben Mee 7
Slipped up early on when Lamptey went close, but as assured at the back as ever on his return. Stood up to the physicality of Welbeck, would often stick his head in where it hurts and made a vital block in the second half to keep Maupay out.