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Gillingham's dismal end of season continued in the biting cold at Turf Moor on Saturday where their winless sequence was extended to six games.
Severely depleted by injury, Gillingham were forced to play with just one recognised striker in Mamady Sidibe up front against a side with one of the worst defensive records in the Nationwide League, Division 1.
Two set-piece goals saw Burnley to victory.
Top scorer Gareth Taylor opened the scoring with his 15th league goal of the season in the 29th minute when he volleyed home from close range after Ian Moore had crossed the ball back when the Gillingham defence failed to clear Matthew O'Neill's long throw.
Another O'Neill long throw presented Drissa Diallo with Burnley's second in the 50th minute.
Midfielder Danny Spiller was outstanding on his second full debut for Gillingham.
Attendance: 14,031.