The Glovers were the stronger side in the first half and Bradford had to put bodies on the line as Matt Kilgallon chested a fiercely-struck Tom James half-volley away inside the six-yard box.
The visitors improved after the break but it was Yeovil who made the breakthrough on 61 minutes. Otis Khan played in Barnes one-on-one on the counter and the man who only joined on Friday coolly slotted in.
Paul Taylor was inches away from an equaliser when his dipping shot from distance hit the underside of the bar before goalkeeper Artur Krysiak recovered brilliantly to save Shay McCartan’s follow up.
In the 76th minute it was 2-0 to the hosts when Francois Zoko broke forward with purpose and set up Jordan Green to sidefoot in a second, before James denied a Bantams consolation by heading a Daniel Devine shot off the line late on.
Rangers manager Steven Gerrard is weighing up a move for Liverpool full-back Jon Flanagan, reports claim.
Scottish champions Celtic are reportedly ready to offer full-back Calvin Miller a new deal before sending him out on loan.
Everton target Jack Wilshere has sparked a scramble for his signature after confirming he is leaving Arsenal this summer.
Tottenham's hopes of landing Wilfried Zaha have been hit by the news Crystal Palace have offered him a bumper new deal to stay.
Ryan Giggs says Gareth Bale would be the perfect fit for Manchester United but has doubts over whether he will leave Real Madrid.
Manchester City's attempts to sign Riyad Mahrez could be in doubt again as reports claim Leicester only want a straight cash deal.