Bradford scored just 47 seconds after the interval when fine play by Garry Thompson set up Ritchie Jones to side-foot a perfect shot low inside Chris Neal's left-hand post from 16 yards.
Vale fans were incensed in the 53rd minute when Jennison Myrie-Williams was booked for diving after he looked to have been tripped in the penalty area by Carl McHugh.
And it turned out to be a big call by referee Darren Drysdale as Craig Forsyth tucked a 14-yard shot inside Neal's right-hand post following more excellent work by Thompson just two minutes later.
Robbie Blake missed from the penalty spot as Doncaster crashed out of their second cup competition in the space of four days, losing 5-3 to Crewe following a 1-1 draw.
Chris Brown's last-gasp goal cancelled out Mathias Pogba's first-half strike to take 10-man Crewe to penalties. But Blake smacked the crossbar with his spot-kick as the Alex held their nerve and tucked away every penalty.
Coventry clinched a place in the semi-finals with a 4-1 win on penalties against Sheffield United after the match finished 1-1 in normal time.
In a tightly-fought contest at the Ricoh Arena, it took a Harry Maguire own goal in the 57th minute to break the deadlock, but United drew level in the 80th minute through David McAllister.
Maguire's night got even worse when it came to penalties as he saw his spot-kick saved by goalkeeper Joe Murphy and then Ryan Flynn blasted over, allowing John Fleck to send Coventry through.
The fourth Northern Area fixture of the evening between Bury and Preston North End was postponed.
Southend surged in to the Southern section semi-final of the Trophy with a shock 2-1 win over League One Brentford at Roots Hall.
The Shrimpers withstood an early spell of pressure from the Bees but fought back to open the scoring in the 27th minute, with Tamika Mkandawire scoring for the first time since August 2011.
The on-loan Millwall midfielder, who was being watched by Lions boss Kenny Jackett in the stands, collected a half cleared right-wing cross from Kevan Hurst before bringing the ball back on to his left foot and firing a deflected 20 yard shot in to the bottom left hand corner of the net.
Southend then doubled their lead in the 40th minute as Kevan Hurst`s stunning 25 yard effort arrowed in to the top left hand corner.
After the break, Barry Corr hit the crossbar from 12 yards before the Bees bagged a late consolation when Paul Hayes raced on to a long ball forward from Lee Hodson and fired past Paul Smith.
Ten-man Wycombe are out of the JPT, meanwhile, after a 2-0 loss to Yeovil at Huish Park.
First half goals from Ed Upson and Sam Foley ensured Gary Johnson's side avoided an upset against the League Two Chairboys, who had Matt Spring sent off in the first half.
And Oxford United edged through via penalties following a 1-1 draw at Plymouth Argyle.