The hosts were on course to follow up derby wins over their bitter Glasgow rivals in January and March when Cyriel Dessers scored shortly before half-time against the newly-crowned Scottish champions.
But Idah's second-half leveller extended Rangers' winless run to six games in a row in all competitions.
The Gers, still 17 points adrift of Celtic, have won just four of their 12 games under interim boss Barry Ferguson and none at home since February 2nd.
There was no guard of honour from the Rangers players in honour of Celtic's latest title triumph, but Brendan Rodgers' visitors were roared on to the pitch by some 2,100 of their own supporters.
It was the first time away fans had attended an Ibrox derby since a 2-2 draw in January 2023.
Rangers thought they had gone ahead in the 24th minute when Nicolas Raskin got his head to a James Tavernier free-kick and nodded beyond Viljami Sinisalo.
However, the goal was eventually disallowed following a VAR review after the Belgian was ruled to have strayed offside.
Celtic began to make their presence felt and Cameron Carter-Vickers's header from Arne Engels' corner was pushed over by Liam Kelly in the 33rd minute.
The Rangers goalkeeper made another save to deny Idah in the 43rd minute and barely 60 seconds later, Ferguson's men were ahead.
Mohamed Diomande's pass into the box was dummied by Vaclav Cerny for Dessers, who held off Liam Scales and struck a low shot past Sinisalo from just outside the six-yard box.
Celtic, however, drew level in the 57th minute.
Daizen Maeda beat Tavernier on the left and as John Souttar tried to deal with the danger, the clearance ricocheted off the Japanese player and fell to Idah.
The 24-year-old Ireland international turned and fired home - with the aid of a deflection off the unfortunate Souttar - from just inside the box.
The goal was swiftly ruled out on the field for offside against Maeda but eventually stood following a lengthy VAR check.
Celtic had a chance to win it late on when Maeda seized on a sloppy piece of play from Tavernier to burst clear, but Kelly ensured the final Glasgow derby of the season ended with honours even.