It has looked likely that a dream introduction from replacement Joe Newell would win the day for the Millers, with the midfielder dramatically firing home with his first touch to put the visitors in front for a second time on 72 minutes.
It arrived shortly after back-up home keeper Rory Watson came onto replace the injured Matt Gilks, with his first duty being to pick the ball out of the net.
But Iron persisted and drew level when Barnsley loanee McGeehan picked the perfect moment to score his first goal for the Iron, bundling in at the second attempt after Marek Rodak had blocked his initial effort after the visitors couldn't clear their lines.
There was plenty of drama much earlier with two goals in the space of 28 first-half seconds setting this tie alight.
Jon Taylor burst past Murray Wallace to net a 17th-minute opener but, almost immediately, the Iron levelled with an unfortunate own goal from Michael Ihiekwe, who diverted Duane Holmes's dinked shot into his own net, despite the effort looking like it was heading wide.
Handed a few selection posers, Millers boss Paul Warne elected to stick with Joe Mattock and Taylor in their respective positions in what probably constituted tight calls and his decision to start with the latter bore fruit by virtue of his opening strike. Warne, however, will have been less happy about his side's concession just half a minute later.
It was a brisk, watchable and competitive half, with Scunthorpe's slick movement causing problems in spells for the Millers rearguard, while the visitors also possessed danger of their own at the other end.
Rodak fielded an early effort from the lively Duane Holmes, but it was the Millers who drew first blood after catching out the Iron rearguard.
Taylor ghosted onto an intelligent throughball from Richie Towell - restored to the hosts' starting line-up in place of David Ball in the Millers' sole change - down the hosts left defensive channel and he steered the ball low past Gilks.
The strike sparked off ecstatic celebrations among the 1,601 Millers contingent, with a red smoke bomb let off. But before the smoke had dispersed, the hosts were level.
A cultured move started when Hakeeb Adelakun nipped in front of Mattock and then dissected the Millers rearguard with an incisive pass down the visitors' left with Holmes sent clear before dinking his effort over the advancing Rodak.
In his attempts to clear, the backtracking Ihiekwe can only divert the ball into his own net after making a mess of his attempted clearance.
The Millers had a scare soon after with Rory McArdle's close-range effort at the far post clipping the woodwork following Josh Morris's deep corner.
Rotherham had to weather a spell of pressure from the pumped-up hosts, but finished the half encouragingly with Towell firing over when well placed.
The early action of the second half saw Scunthorpe display more assertion and ask more questions and they went close with McArdle's point-blank header flying straight at Rodak after some pressure.
The next major development was one that the hosts could have done without, with veteran goalkeeper Gilks forced off with injury after failing to recover from a heavy knock sustained early in the half.
Soon after, his replacement Watson was picking the ball out of the net following Newell's spectacular introduction.
At the other end, Scunthorpe went desperatelyclose to a leveller when Ivan Toney saw his follow-up hit the post after Rodak had parried out Holmes's low drive.
The Millers almost added a late third when Ryan Williams' shot flashed wide, but Scunthorpe had the final say when McGeehan restored parity after a long throw was flicked on by Toney, with the unfortunate Ihiekwe seeming to get in Rodak's way as he attempted to keep out McGeehan's rebound.
Rotherham United: Rodak; Emmanuel, Ihiekwe, Wood, Mattock; Palmer, Taylor (Newell 63), Vaulks, Towell (Ajayi 72), Williams (Forde 90); Smith. Substitutes unused: Price, Ball, Purrington, Lavery.
Scunthorpe United: Gilks (Watson 62); Clarke, McArdle, Wallace, Townsend; Yates, Ojo; Adelakun (McGeehan 75), Holmes, Morris; Toney (Hooper 90). Substitutes unused: Bishop, Novak, Vermijl, Burgess.
Referee: T Robinson (West Sussex).
Attendance: 6,591 (1,601 Rotherham supporters).