The Brazilian ace completed the scoring after 84 minutes with his first goal of the season before being immediately substituted by Mancini.
But if Mancini thought his side were in for an easy ride when Martin Petrov fired them ahead with a thundering shot after only thee minutes, battling Scunthorpe had other ideas in a pulsating tie.
The Championship side took the game by the scruff of the neck for long spells and three times in the first half carved open the City defence.
First skipper Cliff Byrne popped up unmarked at the far post to rattle the bar with a close-range header. Then striker Paul Hayes scuffed a shot just wide for the home side after being set up by a cushioned header from Rob Jones.
But it was third time lucky for Scunthorpe when Hayes equalised in the 29th minute when he volleyed a shot past keeper Stuart Taylor from close range with City looking for an offside flag that never came.
It had been an uncomfortable opening 45 minutes for the Premier League side, but they snatched the lead back just before the interval when a clever ball into the box by Stephen Ireland produced a good side-foot finish from defender Nedum Onuoha.
Scunthorpe so nearly levelled early in the second half when a shot by Sam Togwell forced a fingertip save from keeper Taylor.
A stunning 30-yard effort from full-back Sylvinho put City 3-1 in front after 57 minutes but Scunthorpe were back in the game again 11 minutes later when a shot from Byrne took a deflection off City centre-back Dedryck Boyata as it squeezed past Taylor.
Scunthorpe threw everything forward in search of an equaliser before Robinho finally ended their hopes.