A victory for the home side would have confirmed Bristol City in second place with a seven-point advantage over Yeovil Town and Nottingham Forest.
But, after scoring first, they were outplayed as their Brazilian keeper, Adriano Basso let in two goals over his head.
Both sides could have had an early goal; Bristol when Brian Wilson was brought down inches outside the box and Bradford when Basso spilled a long shot from Marc Bridge-Wilkinson.
A misconceived clearance by Bradley Orr set up the Bradford chance but the right-back was the inspiration behind the Robins' 13th-minute goal.
Playing with three at the back, the Yorkshire side had a big gap down the right flank, where wing-back Ben Parker was far too far forward.
Orr put a ball into the gap, Enoch Showunmi carried it on to the by-line and chipped the keeper to present Phil Jevons with his season's 17th goal.
As the pressure stayed on them, Bradford picked up cards for Craig Bentham and Moses Ashikodi but hauled themselves into the game right on half-time.
Billy Paynter chested the ball down and his 35-yard shot caught Basso cold as it flew in.
Bradford then took a grip on the game in the first ten minutes after the break.
First, Joe Colbeck raced 45 yards down the right flank to set up a tap-in for Ashikodi.
Then, in the 55th minute, another long-range shot, this one by Steven Schumacher, caught out Basso again and Paynter was there on the line to confirm the ball was in.
The home side grabbed an injury-time goal back through Alex Russell, but they were well beaten on the night.
A late leveller from substitute Poul Hubertz spared Millwall's blushes as Dario Gradi's Crewe almost staged a late smash-and-grab raid in a four-goal thriller at The Den.
In a flurry of late drama, Crewe left-back Darren Moss scored against the run of play to put the visitors ahead six minutes from time, before super-sub Hubertz forced home an injury-time equaliser to extend Millwall's unbeaten run to four games.
A nip-and-tuck encounter had earlier seen Crewe open the scoring through Michael Higdon, before Millwall struck back on the brink of half-time as Darren Byfield headed home the 14th goal of an increasingly impressive season.
A second-half surge from Millwall should have seen them put the outcome beyond doubt long before Moss' intervention but, despite the outstanding efforts of attacking livewire Byfield, Willie Donachie's men could not break down a stubborn Crewe defence.