A superb, high-energy first-half performance from Rangers threatened to blow their hosts away, as they exploited the injury-enforced absences of Celtic captain Callum McGregor and centre-backs Auston Trusty and Liam Scales.
That meant Maik Nawrocki came in for his first start of the season, having had just 23 minutes of cup football this term.
And the recast defence took just four minutes to concede when Raskin got above Jeffrey Schlupp to flick in James Tavernier's corner.
By the time Diomande, unmarked inside the box, found Kasper Schmeichel's right-hand corner just before the break, Rangers could have been even further ahead.
Unusually edgy goalkeeper Schmeichel had earlier passed straight to Vaclav Cerny, only for the Czech international to delay shooting and waste the chance.
Two down at the interval, Celtic needed to respond positively and they did.
Maeda, shifted to the flank to accommodate the interval introduction of Adam Idah, leapt high above Tavernier to head in Jota's cross just after the restart.
A well-worked team goal then drew Brendan Rodgers' side level, when Luke McCowan set up Hatate to slip a finish across Jack Butland and into the net.
It looked like the reigning champions could go on and secure the comeback win that would leave them just two victories from retaining the title.
But instead it was Igamane who struck, condemning Celtic to a first domestic home defeat since the league loss to Hearts in December 2023.