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.
Cardiff remain unhappy with Derby's decision to postpone Sunday's Sky Bet Championship game at Pride Park.
Dundee United boss Csaba Laszlo has been left hoping for St Mirren to slip up in the race to seal promotion to the Ladbrokes Premiership.
Crewe will consider starting Chris Dagnall when they host Forest Green on Tuesday.