Any hopes of an upset, fuelled by East Fife's eight-game unbeaten run and injury-hit Dunfermline's recent struggle for form, were immediately dashed as Barry Nicholson and Noel Hunt set up Tod for a looping header which deceived keeper Scott Morrison to give the big utility player his eighth goal of the season.
The contest might have been all over in the eighth minute but Morrison made a double save from Hunt and Gary Mason before Nicholson blazed a third attempt over the bar.
East Fife's heads finally cleared and Steven Nicholas and top scorer Brian Fairbairn kept the home defence busy without seriously threatening while Dunfermline fell into the trap of trying too many long-range shots with Hunt and Darren Young the main culprits.
Hunt produced a better effort which was blocked by Morrison after 33 minutes and headers from Scott Thomson and Mason maintained Dunfermline's hold on the game.
The visitors made a storming start to the second half, but when Derek Stillie saved a 15-yard shot from Sean Paliczka their last chance had gone.
The Pars piled on the pressure and, after near misses for Young and Dempsey, Hunt side-footed home the killer second goal.
Another wonder save from Morrison denied Young yet again and Dempsey somehow hit the bar from six yards but the minnows were by now totally drained and Dempsey made it 3-0 with just over 20 minutes left.
East Fife substitute Leslie Byle pulled one back with a glancing header deep into injury time.