A win over the faltering Londoners would have seen the Bantams jump out of the bottom four with two games to go, but strikes from Gary Alexander and Adam Tann punished City's wasteful finishing.
Welsh international keeper Glyn Garner made four crucial first-half saves as City dominated the play, but Bradford shot themselves in the foot after the break.
Garner produced a stunning save after just eight minutes when he blocked Billy Paynter's 14-yard strike, and he made up for a Matthew Lockwood mistake by grabbing Omar Daley's angled shot in the 16th minute.
Although City's keeper Donovan Ricketts had a few self-inflicted scares the O's produced little going forward until striker Alexander fired over the bar from eight yards after a great run by Lockwood.
But City should have taken the lead after 25 minutes when the speedy Daley burst clear down the left flank only to fire into the brave Garner with his unmarked teammate Spencer Weir-Daley screaming for the pull-back on the penalty spot.
Weir-Daley, who was making his first start since his loan move from Nottingham Forest, finally got a sight of goal himself after 40 minutes when he raced onto Paynter's header, but with Garner stranded in no man's land he lobbed the ball wide of the empty net from 20 yards.
As the anxiety increased, City struggled to play as well after the interval and the O's rocked them after 62 minutes when Alexander fired in his 12th goal of the season.
Substitute striker Jabo Ibehre used his strength to hold off two would-be tacklers before sliding the ball into Alexander who drove a fierce left-foot shot into the roof of the City net from 10 yards.
The City fans were still reeling from that blow when the visitors doubled their tally through full-back Tann.
Winger Shane Tudor won a free-kick on the right and when skipper John Mackie headed his cross back from the far post Tann reacted first to lash the loose ball home from just outside the six-yard box.
The double strike knocked the stuffing out of David Wetherall's side and despite their perilous position they failed to create any momentum in the final quarter.