The game at the LNER community stadium on a windy Sunday would get off to a fast start for Barnsley as Pierreponts excellent corner was headed home by Louise Biggins to give Barnsley the lead after only four minutes.
Barnsley would continue to put pressure on the home team however weren't able to get a second before the break.
The second half got off to an even start before Nat Watson was shown a straight red card, just before then hour mark, for a challenge on the last line of defence.
However moments later Barnsley would win a penalty which Rosie Axten would step up to take, although her first effort was saved, she followed in to double Barnsley's lead and put the away side in control of the tie.
Only two minutes later it was three-nil when Louise Biggins got her second of the match and her third in two weeks.
Right towards the end of the match freshly off the bench Jodie Nelson got Barnsley's fourth and wrapped up the three points.
The reds don't have a game next week before they travel to Chorley on the 21st April.