Ibanez scored a stunning late winner as Roma came from behind to take command of their Europa League quarter-final with Ajax with a 2-1 first-leg win in Amsterdam.
Roma looked to be heading for a damaging defeat when Davy Klaasen put Ajax ahead in the 39th minute and Dusan Tadic won a penalty shortly after the restart.
But Pau Lopez saved from 12 yards before European debutant Kjell Scherpen's huge error at the other end allowed Lorenzo Pellegrini to equalise.
And a late moment of magic from Ibanez turned the tide firmly in Roma's favour, the defender unleashing an unstoppable volley to give the Serie A side the lead in the tie going into next week's return leg.
Edin Dzeko fired past the left-hand post and Bryan Cristante forced Scherpen into a fine diving save with a powerful long-range effort as Roma started brightly.
Tadic spurned Ajax's first clear-cut opportunity at the end of a well-worked move but he was key in helping the hosts take the lead six minutes before half-time.
Klaasen pounced on Amadou Diawara's sloppy pass towards his own goal and fed Tadic, whose return pass presented the midfielder with the simple task of slotting into an unguarded net.
Soon after picking the ball out of his net, Lopez had to be alert to prevent Antony from doubling the deficit and his decision to stand his ground in the middle of the goal when faced with a Tadic penalty seven minutes into the second half paid dividends as he palmed away the spot-kick after the forward was fouled by Ibanez.
And Ajax were duly punished for Tadic's failure to convert, though he would have expected Scherpen to handle Pellegrini's relatively tame free-kick instead of fumbling it over the line.
Lopez was almost guilty of a similarly egregious error when he spilled a seemingly innocuous effort from Nicolas Tagliafico, but he was soon back to his best to smother after Brian Brobbey came through on goal.
He then turned an Antony volley over the crossbar as Ajax tried and failed to reclaim the advantage, before then being dealt a major blow three minutes from time when Pellegrini's corner was deflected into the path of Ibanez, who controlled it brilliantly with his chest and sent a scorching volley beyond a helpless Scherpen and into the roof of the net.
What does it mean? Fonseca given lifeline
Roma coach Paulo Fonseca is expected to leave the club if they do not qualify for the Champions League.
Seven points adrift of fourth-placed Atalanta in Serie A, the Europa League may be their best hope, and it looked to be slipping through their fingers as Tadic put the ball down on the spot.
But Lopez kept them in it and, after a helping hand from Scherpen and the brilliance of Ibanez, Fonseca's odds of leading Roma to the Champions League are very much improved.
Ibanez the unlikely hero
When he tripped Tadic to concede the penalty, Ibanez appeared set to play a critical role in a defeat for Roma. But his blushes were spared by his goalkeeper, and he more than made amends with a goal that will live long in the memory.
Scherpen's horror show
Scherpen only made his debut on Sunday due to an injury to Maarten Stekelenburg, and the inexperienced Ajax keeper's European bow could hardly have gone worse. He made only two saves and Roma scored from each of their two shots on target in the second half. Though he could do little about the second, it was his horrendous mistake for the first that set in motion a previously unlikely comeback.
The teams reconvene in Rome next Thursday. Before then, Ajax visit RKC Waalwijk in the Eredivisie on Sunday, when Roma host Bologna in Serie A.