Rangers, quite remarkably, found themselves 3-0 down early in the second half before launching a barnstorming comeback that brought about two Kris Boyd goals but couldn’t yield an equaliser.
It leaves the new manager, in all likelihood Walter Smith, with much to contemplate and with only the UEFA Cup remaining as a realistic trophy target this season.
Durrant, in what will probably be his one and only match in charge, had been forced into making several changes with Jeremy Clement, Libor Sionko and Dado Prso all unavailable through injury or suspension.
It meant a return for Julien Rodriguez at the heart of the defence – Brahim Hemdani moved to a central midfield role – while Charlie Adam and Barry Ferguson also returned to the side, although Gavin Rae retained the captain’s armband.
After a quiet start, Rangers squandered two golden opportunities to go in front. Both came from headers, Karl Svensson lacking the power and direction to beat Roddy McKenzie from around six yards before Alan Hutton’s back post connection with Charlie Adam’s cross was blocked, perhaps with an arm, by Owen Morrison.
Perhaps fortunate not to have conceded a penalty, the Nothern Irishman turned provider moments later as Dunfermline went in front with their first real attack of note.
Morrison’s cross fell nicely for Jim Hamilton who was lurking unmarked at the back post and he finished adroitly under Allan McGregor.
It was Dunfermline’s first goal in five matches and another blow to a Rangers side looking for a fresh start following the departure of Paul Le Guen.
Rangers were soon appealing for another penalty when Nacho Novo was upended by goalscorer Hamilton but instead referee Iain Brines deemed the Spaniard the culprit and booked him for diving.
It would get worse for Rangers shortly after when Dunfermline extended their lead. Stephen Simmons’ initial shot was blocked by Svensson but the rebound ricocheted off Ian Muray into his path and the former Hearts man made no mistake second time around.
The half-time interval offered Rangers the chance to regroup to try to find a way back into the tie but instead they found themselves further behind less than two minutes into the second half.
Scott Morrison swung in the corner from the right and Phil McGuire jumped highest to nod his side into an incredible 3-0 lead.
That seemed to be it for Rangers’ cup ambitions for this season but Kris Boyd offered a lifeline when he bundled Rae’s cross past McKenzie to reduce the deficit.
Rangers, finally playing like they were interested, thought they had a second just after the hour mark only for Boyd’s header to be ruled out for an infringement but the striker would not be denied just five minutes later.
A poor Dunfermline clearance fell kindly for Murray and his fantastic cross was nodded high into the roof by Boyd to bring Rangers within touching distance of salvaging this tie.
They should have been level just three minutes later, Ferguson heading Burke’s cross on to the top of the bar when it looked easier to score and then Boyd sliding his shot agonisingly wide of the far post after latching on to Burke’s visionary pass.
Rangers were piling on the pressure and Burke was at the heart of it all. Another cute pass sent Ferguson scampering through on goal but McKenzie stood up well to block his shot.
RANGERS (4-4-2): McGregor; Hutton, Rodriguez (Burke 34), Svensson, Murray; Rae, Ferguson, Hemdani, Adam (Buffel 63); Novo, Boyd
Subs not used: Gallacher, Lennon, Papac
Booked: Novo (23), Boyd (35), Adam (37), Hutton (90)
DUNFERMLINE (4-4-2): McKenzie; Ross, Wilson, McGuire, S Morrison; O’Brien (Bamba 76), Young, Simmons, O Morrison (Woods 66); Crawford, Hamilton (Daquin 82)
Subs not used: Murdoch, Tod
Booked: Simmons (30), Wilson (89)