The front four of Igamane, Vaclav Cerny, Nedim Bajrami and Ianis Hagi pulled apart a ragged Hibs backline in an electric opening, during which the visitors scored twice.
Hagi firstly teed up Igamane to finish emphatically after just four minutes before Bajrami crossed for the Moroccan striker to power in a header.
Clement's men should have been out of sight by the time Hibs gained any kind of composure.
But just seconds after the VAR officials looked at a potential red-card challenge from Mohamed Diomande on Nicky Cadden, Martin Boyle dragged a finish into the far corner.
And the game was level just after the hour when Hagi bundled over Josh Campbell, allowing Boyle, who rolled back the years with a stunning display, to smash in from the spot.
Rangers thought they had three points back in the bag when the superb Igamane again finished first time from a Vaclav Cerny cross.
But Bushiri capitalised on unconvincing goalkeeping from Liam Kelly to head in from a corner nine minutes later.
There was time for Igamane to crack the far post and Boyle to curl just wide in an incredible finale, but an epic encounter would finish level.
It means leaders Celtic can extend their advantage at the top to 13 points when they host St Mirren later on Sunday (15:00 GMT).