Two goals from Chris Killen and one apiece from Ivan Sproule and Abdessalam Benjelloun only told half the story at the Edinburgh side completely outclassed struggling Dunfermline throughout almost the entire match.
The visitors should have gone ahead after nine minutes when Killen had the ball the in the back of the net. But the New Zealand international had been pulled up for offside as he chased Michael Stewart's through ball.
Five minutes later Souleymane Bamba did well to clear another Killen effort on the line to keep the Pars on level terms. But the pressure on the Dunfermline goal was unrelenting and on 16 minutes Dorus de Vries pulled off a spectacular one-handed save to stop a Rob Jones header.
Midway through the half Dunfermline made a vociferous penalty claim as Mark Burchill claimed to have been brought down by Zibi Malkowski, but their shouts were ignored by referee Mike McCurry.
Hibs eventually made the breakthrough 90 seconds before the interval as the ever-dangerous Sproule chipped the ball over de Vries to make it 1-0.
The second half didn't start off any better for Dunfermline with Stewart hitting the crossbar for the visitors less than five minutes after the restart. And ten minutes later Sproule unselfishly cut back to Killen, who drilled the ball in off the post to make it 2-0.
With less than two minutes remaining substitute Benjelloun linked up with his countryman Merouane Zemmama to scored Hibs' third and Killen rounded off a miserable night for Dunfermline as he added a fourth in injury time.