Leeds came close to opening the scoring when McMaster's free-kick struck Andy Marriotts post but the first half ended goalless.
Barmby had a chance to put the hosts ahead 8 minutes after the break but headed over when unchallenged in the box.
Right on the hour-mark Darren Carter put Blues ahead with a 20 yard drive through a crowd of Leeds defenders following a Blues corner.
Three minutes later Blues doubled their advantage. Tony Capaldi's cross was met by Michael Johnson who headed the ball down into the path of Fagan to shoot past Martyn inside the area.
Keith Bertschin's side defended well from thereonin and came home from Yorkshire with a well deserved three points and their third win on the trot.
Blues: Marriott, Tebily, Vickers, Purse, M. Johnson, Capaldi, Coly, Swierczewski, Kirovski, Fagan, Carter. Subs: Doyle, Arrowsmith, Luntala, Gilbert, Till.
Leeds: Martyn, Richardson, Burns, Keegan, Cansdell-Sherriff, Kilgallon, Barmby, McMaster, Simon Johnson, McPhail, Singh. Subs: McStay, Carson, McDaid, Cronin, Farren, Coyles.