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 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.