Bradford City 2(Webb-Foster 18, Waters 87)
Barnsley 0
The young Reds had a great chance to progress against the ten men of Bradford, after Joe Brennan saw red on 25 minutes, but they failed to take advantage at a windswept Coral Windows Stadium.
The hosts dominated the opening exchanges and should have taken the lead through Mottley-Henry but he hit the side-netting of an open goal on three minutes.
On 18 minutes Webb-Foster made a brilliant run and controlled Pollard's long ball before tucking into the near post for the Bantams' opener.
But, seven minutes later, a scuffle following Joe Brennan's late tackle on Mason Holgate saw the former dismissed for raising his hands towards the Barnsley defender.
The closest the Reds came in the first half was through Holgate as he took aim from over 35 yards but saw his strike fizz a yard wide of the post.
After the break the Reds piled on the pressure as Bradford packed into their own half.
Just two minutes into the second period saw 15-year-old Louis Wardle come close to his second goal in the competition. When Bree diverted the ball into his path from Templeton's cross, he turned over from 10 yards.
Sam Hanna fired a warning shot wide and then Matty Templeton brought a smart save from Barker as the youngsters searched for the equaliser.
The best chance of the second half came on 77 minutes when Mason Holgate, who had pushed up front as a striker for the last 15 minutes of the tie, met Bailey Gooda's superb cross. Unfortunately, Holgate couldn't divert his header on target and nodded over.
With Barnsley dominating, there was always the threat of the counter-attack from City and Wright fired over after a blistering charge forward from Mottley-Henry and Cissa on 78 minutes.
The counter-attack did pay off on 87 minutes as substitute Waters nodded home at the far post with a fine looping header after meeting Mottley-Henry's deep cross.
In stoppage time Mason Holgate tried his luck from a 30-yard free-kick but dragged his low effort wide as the Reds couldn't find the breakthrough.
Teams:
Bradford: Barker, Jenkinson, Kershaw, King, Pollard (c), Devine, Mottley-Henry, Wright, Webb-Foster (Cissa 72), Chippendale (Waters 85), Brennan (s/o 25).
Reds: Rusling, Templeton (Proctor 90+2), Gooda (c), Cowgill, Holgate, Hanna, Bree, Ndlovu (Saeed 60), Alton, Pedro (Goodwin 46), Wardle.
Attendance: 359