Terry Butcher's side banked back-to-back wins thanks to Lee Thorpe's cool finish on the hour, but City boss Stuart McCall must be wondering where his side's next win will come from after picking up just two points from eight games.
The Bantams finally ended their home goal-drought when centre-half Mark Bower forced home a chance late on, but their finishing was second best again in front of another crowd of more than 13,000.
City struggled to make any impression in the early stages and they were stunned after 41 minutes when Poole unleashed a superb dipping left-foot volley which beat keeper Donovan Ricketts from 25 yards out.
The winger opened his league account with a free-kick against Bury in September, but this strike was even better.
It was too good a goal for a disappointing first half, but City almost grabbed an equaliser thanks to their dangerman Guylain Ndumbu-Nsungu.
The powerful striker surged from halfway before setting up team-mate Barry Conlon in the six-yard box, but the out-of-luck frontman saw his close-range chance fly wide.
Fired up after the break, City pressed for an equaliser but Bees keeper Simon Brown showed his class with an excellent fingertip save to stop Ndumbu-Nsungu levelling with a looping header.
Conlon bore the brunt of the fans' frustration as he wasted other opportunities and City looked dead and buried when experienced striker Thorpe drove in the visitors' second on the hour.
The Bees frontman took full advantage of the time he was given in the City box and he beat Ricketts with another well-struck volley from 14 yards out.
As City faced a sixth defeat in eight games the Bees wasted several chances to pile on the agony.
Thorpe failed to make the most of two great chances and he must have been a worried man when Bower swung a leg at a loose ball two minutes from time to throw City a late lifeline.
The centre-half's goal was the first on home soil in almost six hours of football, but hopes of a dramatic finale were dashed as Butcher's men hung on for the win.