Rangers started well and were camped inside the Barnsley half for the opening 10 minutes before the home side eventually grew into the game but could not fashion themselves any chances.
The first action of note came in the 26th minute when Barnsley got their opportunity to open the scoring.
Callum Styles attempted a through ball into the path of Woodrow. Barbet slid in to make the interception, but the ball still managed to find its way through to Barnsley's top goal-scorer and defender Rob Dickie pulled him down when it looked for all the world Woodrow would score.
The QPR centre-back was sent off as a result for being the last man, then Woodrow stepped up and converted the spot-kick to get his fourth goal of the season.
Ten minutes later and Chaplin doubled the lead for the Tykes. A pass was played into Woodrow and with a deft little flick he played in Dominik Frieser. The Austrian cut the ball back to Chaplin, who after a heavy touch to make himself the space, squeezed the ball in at the near post despite Seny Dieng's best efforts in the QPR goal.
Six minutes after the restart and Barnsley should have made it 3-0. A wonderful cross in from Alex Mowatt found Chaplin unmarked six yards out. The striker tried to chest the ball into the net for his second goal of the game but didn't make enough meaningful contact and the ball just fell to Dieng.
Twenty minutes into the second half and the win was wrapped up for Barnsley.
Frieser found Woodrow inside the area, but his touch was heavy and evaded him. Anticipating a challenge from the striker, Barbet stuck out a foot to put in a challenge but diverted the ball past his own keeper to compile the visitors' misery.
Barnsley had a number of chances in the final 20 minutes to add to their tally. Substitutes Patrick Schmidt and Elliot Simoes saw efforts saved by the Rangers stopper, who was resolute in the final stages.