Left-winger Michael McIndoe missed a couple of chances to get his name on the scoresheet early on after good build up play by Rovers.
Neil Roberts then set up Gregg Blundell to give Rovers a 1-0 lead after 16 minutes.
Blundell grabbed his second after half-an-hour thanks to another assist from Roberts before a crunching tackle by Vaughan on James Coppinger made the Barnsley-man see red and end his teams hopes of a comeback.
Doolan hit a 25-yard-screamer to make it 3-0 and 6 minutes from time, Green rubbed salt in the wound of Barnsley to make a 4-0 win for Rovers.
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