The skipper struck a lovely free-kick from 30 yards nine minutes from time to cause a minor upset against the League One MK Dons.
Omar Daley had given the Bantams an early lead only for Jemal Johnson to respond just before the break.
But Lee's late strike was no more than they deserve after a spirited performance and made sure there wouldn't be a replay - which neither side would have wanted.
Bradford stunned the Dons by going ahead after just 90 seconds. The defence looked half asleep as Daley cut in with ease past Shaun Cummings and just kept on running unchallenged before lashing the ball in the far bottom corner.
It shocked the home side who just couldn't get going and struggling to create any attacking presence.
Although from one rare corner, Jude Stirling rose majestically and had a header cleared off the line.
It looked like Bradford would take a deserved lead into the break when from nowhere Johnson cut in on his left foot and hit a stinging shot in the bottom right hand corner - completely taking Rhys Evans by surprise.
Dons took over second half and Ali Gerba may have done better after Johnson's deft touch put him through on goal, but Evans did well to force him wide before blocking his shot.
Mark Wright also had a decent effort as he curled over from 15 yards, but Bradford started to rally late on with Nicky Law having a decent effort before Lee struck.
Then Miguel Llera brought down Michael Boulding when clean through on goal.
To the shock of the crowd he was only given a yellow but justice was served in the end as Lee walloped home a low free-kick from 30 yards.
Dons did have a chance late on with a free-kick of their own on the very edge of the box, but Gerba hit a dreadful shot miles over.