James Collins opened the scoring from the penalty spot just before half-time while Tom Barkhuizen and Jason Knight also hit the target for the in-form Rams.

Barnsley had made a fast start to the first FA Cup meeting between the clubs in 125 years and almost went ahead in the fourth minute when Tom Edwards’ header was superbly saved by Joe Wildsmith.

Derby, unbeaten in 90 minutes in all competitions since October, gradually settled and went close in the 24th minute when Lewis Dobbin’s header glanced off the bar.

TOUGH TRIP: Barnsley's Nicky Cadden (right) is challenged by Derby County's Jake Rooney at Pride Park on Sunday afternoon. Picture: Gareth Copley/Getty Images.

And they took the lead in the 45th minute after Matthew Wolfe handled from a corner and Collins converted the penalty.

Derby doubled their lead on the hour after Barnsley failed to clear and Barkhuizen fired into the roof of the net from 15 yards.

The tie was over in the 79th minute when Barnsley were caught trying to play out from the back and although Nathaniel Mendez-Laing’s first shot was saved, he rolled the rebound to Knight to drive in the third.

Barnsley crash out of FA Cup at hands of Derby County