After failing to break the deadlock during a dominant first-half display, Italy went ahead in the 55th minute when Federico Bernardeschi's long-range drive was inexplicably spilled into his own net by Andriy Pyatov.
Ukraine, who had scarcely offered anything in the way of attacking threat prior to falling behind, secured a draw thanks to a volley from Ruslan Malinovskiy, who also saw a late free-kick cannon back off the crossbar.
Pyatov's outing started in more positive fashion and he twice denied Italy in the opening stages, pawing away Bernardeschi's curling drive and then brilliantly repelling Leonardo Bonucci's hooked volley from 12 yards.
Lorenzo Insigne clipped wide after being found inside the penalty area by Federico Chiesa midway through the first half before Pyatov tipped over Nicolo Barella's whipped effort from 25 yards.
Italy were unable to make their superiority count before the interval as Pyatov once again denied them, this time pushing Chiesa's low drive past his right-hand post.
However, Mancini's side took the lead their dominance deserved 10 minutes after the interval when Pyatov made a mess of Bernardeschi's attempt from distance.
Out of nothing, the visitors pulled level seven minutes later when Malinovskiy's volley nestled in Gianluigi Donnarumma's bottom-left corner.
Malinovskiy then thumped a stunning free-kick against the woodwork, while Donnarumma kept out Taras Stepanenko's header to at least make sure Mancini avoided a first defeat on home soil.
What does it mean: Scale of Mancini's task now clear
Mancini was expected to inject new life into Italian football after their humiliating failure to qualify for the 2018 World Cup, but it is not going according to plan for the former Manchester City boss. Ukraine, in contrast, look in far better shape and are now unbeaten in eight under the guidance of Andriy Shevchenko.
Malinovskiy opens international account
Italy looked to be on course for a deserved win before the Genk midfielder scored his first international goal with a composed finish. It could have got even better for the 25-year-old too, had his set-piece attempt in the closing stages found the net.
Pyatov endures mixed night
The Shakhtar Donetsk goalkeeper was outstanding in the first half, keeping Italy at bay with a string of fine stops, but he will have nightmares about Bernardeschi's effort that spun out of his hands and into the net.