Dunfermline booked their place in the fourth round of the William Hill Scottish Cup after recording a 1-0 victory over fellow Ladbrokes League One high-flyers Ayr.The visitors broke the deadlock in the 22nd minute when Andy Geggan scored his fourth goal of the season from range.Ayr began to push as the first half wore on, with Alan Trouten forcing a brilliant save from Pars goalkeeper Sean Murdoch in the 29th minute.Faissal El Bakhtaoui had a chance to increase Dunfermline's lead in the 55th minute when he chanced his arm from the right side of the box but Greg Fleming produced a save to keep him out.