Burnley proved their midweek victory over Manchester United was no fluke as they beat Everton at Turf Moor for back-to-back 1-0 home wins.
Wade Elliott's 34th-minute strike gave the Clarets their second Barclays Premier League top-five scalp inside four days.
The midfielder and Martin Paterson had both fluffed their attempts at Robbie Blake's right-wing cross but Steven Fletcher turned the ball back to Elliott and as no-one closed him down he picked his spot just inside Tim Howard's right-hand post and curled home his shot.
Everton striker Louis Saha missed a controversial second-half penalty which had wrongly been awarded after Tony Hibbert went down in the area.
The Clarets had gone close to scoring after just 40 seconds when a Martin Paterson header rebounded off the crossbar. The ball dropped to Steven Fletcher who forced the American into a low save.