Shakhtar Donetsk reached the quarter-finals of the Champions League for the first time in their history as they saw off 10-man Roma 3-0 to seal a 6-2 aggregate success.
A first-half goal from Tomas Hubschman put them in control and Roma made their task all but impossible as Marco Borriello saw his penalty saved by Andrei Pyatov and centre-half Philippe Mexes then saw red for picking up two needless bookings.
Willian's lovely strike doubled Shakhtar's lead and substitute Eduardo rounded things off late on as the visitors endured a miserable night.
Shakhtar had caused a major upset by winning the opening leg 3-2 at the Stadio Olimpico and Roma had since parted company with manager Claudio Ranieri, with Vincenzo Montella now in charge.
The former Italy striker had been confident of turning the tie around but Roma were totally outplayed and now have no hopes of securing silverware this term.
The Serie A side had started in reasonably assured fashion.
John Arne Riise drilled an ambitious free-kick effort during a slow opening but it did not take long for the contest to come to life.
The hosts opened the scoring in the 17th minute as Hubschman got the faintest of touches to flick home a whipped cross from Willian to leave Roma needing to score three goals to have any chance of progressing.
The Italians sought a quick response and were furious when the referee failed to point to the spot after a clumsy challenge on Borriello.
Shakhtar goalkeeper Pyatov then made a fine save from Mirko Vucinic shortly before Mexes picked up his first booking for a challenge on Adriano.
Roma should have given themselves a lifeline when Henrikh Mkhitaryan was adjudged to have pulled Borriello's shirt in the box, but the striker's spot-kick was saved low to his left by Pyatov.
Vucinic blazed over the bar before Roma's hopes suffered a further blow as Mexes was given a second yellow by World Cup final referee Howard Webb for a needless challenge on Adriano five minutes before the break.
Borriello headed over from David Pizarro's cross shortly after the resumption, while Alexander Doni beat away a Mkhitaryan effort.
The hosts then put the tie to bed as Willian beautifully curled home after a Darijo Srna corner had run through to the far edge of the penalty area in the 58th minute.
With the game over as a contest the final 30 minutes saw little in the way of goalmouth action, but Eduardo managed to get on the scoresheet as he seized on a poor defensive back pass to coolly slot home beyond Doni with three minutes to play.