The Pars had to win to take the duel to avoid the drop to the final day, but a point was enough for second bottom Hibs.
In the end Dunfermline disappeared with barely a whimper.
The visitors conceded three times in the opening 15 minutes as Matt Doherty exposed their defensive failings, firstly heading in after five minutes before crossing for an unmarked Eoin Doyle to score the second six minutes later.
Garry O'Connor converted on his 29th birthday for his 16th goal of the season after Austin McCann fouled Paul Hanlon, who volleyed in a fourth after 81 minutes.
Replays suggested Hanlon's strike should not have counted, but few at Easter Road cared as Hibs celebrated just a second home win of the SPL season and survival.
The capital club can now focus on the May 19 William Hill Scottish Cup final with Hearts and write off Saturday's trip to Inverness.
Dunfermline, meanwhile, play Kilmarnock next weekend before returning to the Irn-Bru First Division after one season in the top flight, former Hearts manager Jim Jefferies unable to pull off the great escape.
Jefferies, who had claimed six points in six matches prior to Monday night's journey across the Firth of Forth, was consoled by his long-time lieutenant Billy Brown, who is now assistant to Pat Fenlon at Hibs, at the final whistle as the hosts breathed a collective sigh of relief.
Captain James McPake returned from a groin injury in a welcome boost for Hibs, who were without suspended striker Leigh Griffiths, with Doyle his replacement.
The hosts were able to welcome back Lewis Stevenson after a ban saw the midfielder miss the 2-1 win at Aberdeen, a victory which, coupled with the Pars' 0-0 draw at Inverness, saw Hibs open up a five-point lead at the foot of the table.
McPake, one of eight loan players reinforcing the Hibs ranks, saw his parent club Coventry relegated this term and was determined not to suffer the same fate in Edinburgh.
After Martin Hardie and Kyle Hutton shot weakly from long range for Dunfermline, McPake made a crucial contribution to set up the opening goal.
McPake flicked on Tom Soares' free-kick and Doherty stole in at the back post to head across goal and in off the upright.
It was the kind of set-piece goal Dunfermline have been conceding all season and right-back Doherty's second since joining on loan from Wolves, who dropped out of the English top flight.
Andy Dowie shot over from a corner as the Pars sought an immediate response, but soon they were two down as Doherty turned provider.
After evading attempted tackles from Paddy Boyle and McCann, Doherty crossed for an unmarked Doyle to head in.
Four minutes later Hibs had a penalty after McCann was booked for manhandling Hanlon and O'Connor sent Chris Smith the wrong way from the spot.
Mark Brown saved with his legs from Jordan McMillan and denied the Pars right-back again when he met a Boyle cross from the left before a fine McPake cover tackle denied David Graham.
A Stevenson shot lacked conviction before O'Connor came close in the second half, but dragged his effort wide.
Isaiah Osbourne set up a glorious opportunity for a fourth, but Doyle was unable to connect a yard out.
Brown scrambled clear a Hardie free-kick which bounced back off the post moments later.
Hibs were more fortunate after hitting the woodwork when Hanlon was awarded a goal for his spectacular volley, which came down off the underside of the bar.
There was a momentary delay before the officials awarded the goal, but replays suggested the ball had not crossed the line.
The incident could not dampen Hibs' joy as Dunfermline dropped out of the top flight.