Substitute Eddie Johnson looked to have thrown the Bantams a lifeline when he slotted home a cool finish 12 minutes from time, but despite the ball getting a flick on from Yeovil's Jean-Paul Kalala the effort was eventually ruled out for offside.
The Bantams were already two-down thanks to Davies' two clinical finishes, but hopes of a late comeback were dashed when referee Graham Salisbury disallowed Johnson's strike after lengthy discussions with his assistant.
Bradford's protests were instant and sustained, but their misery was compounded when their speedy front man Jermaine Johnson was red-carded for his comments to the referee.
The Bantams, who had drawn their last three home games, started brightly with their new Jamaican international winger Omar Daley impressing, but Davies hit them with the first of two-sucker punches after just five minutes.
The midfielder raced onto Anthony Barry's pass and held off a challenge from City skipper David Wetherall to fire home a low right foot shot from 12 yards.
Bradford responded with some good approach play, but Glovers skipper Terry Skiverton was in commanding form at the heart of their defence, and keeper Steve Mildenhall was only troubled on a couple of occasions.
The Yeovil stopper was tested more after the break and twice denied Jermaine Johnson with good saves.
As City pushed forward looking to grab an equaliser, Yeovil punished them with another sweeping counter attack and Welsh international Davies coolly driving home from an acute angle after 67 minutes.
Yeovil's on-loan hot-shot Leon Best came close to adding to his goal tally with a late shot which fizzed wide.
Despite the efforts of Jermaine Johnson and new man Daley, City struggled to create any clear-cut openings until Eddie Johnson's controversial strike.
Johnson's sending off knocked the stuffing out of City, and manager Colin Todd will be anxiously waiting to find out how long a ban his star man will get.