Xavier Barrau's first goals for the club had given the Bantams hope that they could at last put an end to the miserable home run which has been largely responsible for their perilous plight.
But Craig's leveller 20 minutes from time ensured that the long-suffering Valley Parade faithful have not witnessed success since Chesterfield were dispatched before Christmas.
This game had the distinct feeling of being a meaningless end of season affair and after a minutes silence in memory of the victims of the Bradford City fire - which was impeccably observed - both sides were slow out of the traps.
City's Omar Daley and the lively Darren Byfield both fired shots high into the stands and when a decent chance presented itself to Joe Colbeck after 25 minutes he shot tamely at visiting keeper Lenny Pidgeley.
Just when it looked like the sides would go in at half time all square Barrau caught full-back Danny Senda dozing in his own area.
The Frenchman picked his pocked before rifling a shot past Pidgeley to give the Bantams an unexpected lead.
But it lasted barely a minute into the second half as a neat through ball from substitute Ben May left the home defence flat-footed and Byfield was hand to finish.
The second period proved to be more watchable than the first and a slick counter-attack saw City regain the lead.
Millwall's defence found themselves three against three as the pacy Daley led the charge forward. He fed Colbeck who in turn played a slick ball to Barrau to grab his second goal on his first start for the club.
But again the hapless Bantams could not hold on to their lead for very long. Hopeless marking at the back allowed full-back Craig to ghost in at the far post from a free-kick close to the by-line.
His side-footed effort lacked power, but was good enough to find a way under the body of diving goalkeeper Donovan Ricketts to leave the home supports still waiting for that elusive home win.