Rochdale had to play for most of the second period with 10 men after Joe Rafferty was shown a red card.
Barnsley threatened early on when Ben Pearson played the ball to George Maris who chipped it back to him inside the area and Pearson volleyed wide.
Rochdale’s Iain Henderson was nearly gifted an opening when Lewin Nyatanga slipped and left his back-pass short, but Adam Davies was alert to the danger and made an important block.
The visitors lost Rafferty in the opening minutes of the second half when he received his second yellow card of the game following a foul on Scowen.
The opening goal came after 67 minutes when Scowen met a Conor Hourihane corner with a close-range header.
The same pair combined again to make it 2-0 10 minutes later with Scowen scoring with a thumping header.
Mason Holgate added a third goal with six minutes left with with a far-post finish from another Hourihane corner.
Hourihane got on the score sheet himself along with Winnall in stoppage time to complete the scoring.