Goals from Jacob Brown and Kieffer Moore in the 28th and 38th minutes effectively sunk form side Bradford, who arrived with four wins from their previous five League One games.
To make matters worse, City's Adam Chicksen received a straight red for a trip on Brown a yard outside the area as he bore down on goal late on before Alex Mowatt added a third in stoppage time.
With Brad Potts having joined Preston for a Deepdale record Â£1.6m, Brown was handed his place out wide by Barnsley coach Daniel Stendel and Moore was fit after illness to resume his partnership with Cauley Woodrow up front. Australian international Kenny Dougall had to be content with a place on the bench.
Bradford's new loanee centre-back from Leeds United, Paudie O'Connor, was brought straight in by David Hopkin, with George Miller dropping to the bench. The Bantams enjoyed the backing of 3,562 supporters in the North Stand.
It was a quiet opening quarter with Ryan McGowan, impressing in a new role out on the right, heading onto the roof of the net for City as chances proved limited.
Barnsley got the breakthrough in the 28th minute when Mowatt combined with Mamadou Thiam down the left and clipped the ball to the far post where Brown ran in to head home.
Woodrow then got under a cross from Ben Williams and headed over after the left-back had taken a return pass from Thiam.
Williams provided another inviting deep cross which Richard O'Donnel missed but Cameron McGeehan could only force the ball home with his hand and was promptly booked in the 35th minute.
It was not long before it was 2-0 as Barnsley attacked down the right and a delightful back-heel from Thiam enabled Mowatt to knock the ball into the path of Moore, who forced the ball home from close range for his 14th goal of the season.
Moore headed over from Thiam's corner in stoppage time and the Reds went in 2-0 ahead.
Paudie O'Connor was replaced by Miller at the break and he went into midfield as the Bantams switched to 4-3-3.
But it was Barnsley who pressed in the early stages with Moore flashing a header narrowly over.
Liam Lindsay was booked for pulling back Jack Payne but the defender cleared from the free-kick, and Dimitri Cavare countered, forcing a low stop from O'Donnell at the expense of a corner.
Brown went in the book for a foul on Adam Chicksen but city could not capitalise from the free-kick and McGeehan whistled a shot wide at the other end.
Mike Bahre replaced Woodrow for the Reds and Hope Akpan came on for City's Paul Caddis in the 70th minute.
Payne became the first City player in the book for a foul on Mowatt.
Thiam should have made it 3-0 in the 73rd minute when Cavare headed over a static defence but he hit wide from 14 yards.
Bahre teed up McGeehan but he drilled his shot narrowly wide from outside the area.
McGowan went in the book for his challenge on Bahre and Mowatt followed for a touch of retribution before Victor Adeboyejo replaced Moore.
Thiam had another opportunity but O'Donnell went sprawling to his left and diverted the 16-yard shot against the post.
Connor Wood for Payne and George Moncur for Thiam were the final substitutions infront of the 14,962 attendance.
Chicksen went after Bahre threaded the ball through for Brown, who still got his shot away the wrong side of the post. Barnsley still received a free-kick and Mowatt's curling attempt brought a fine diving save from O'Donnell.
Mowatt had the last say, however, as the ball was chipped across from the left and he calmly tucked the ball home asa O'Donnell raced out in the second minute of stoppage time.