Willian (right) scored a fantastic goal at the Donbass Arena
By Saj Chowdhury
Shakhtar Donetsk booked their place in the last eight of the Champions League for the first time as Roma fell apart.
Shakhtar took a first-half lead when Tomas Hubschman got a faint flick to guide in Willian's left-wing cross.
Roma's Marco Borriello then had his penalty saved by Andriy Pyatov after he had been fouled by Henrik Mkhitaryan.
Philippe Mexes was shown a second yellow card for pulling back Luiz Adriano, before Willian curled in and Eduardo slotted in a late third.
The Ukrainian outfit deserved to go through but Roma will count themselves unlucky, having started well before their game plan was ripped apart in 27 madcap first-half minutes.
Having trailed 3-2 from the first leg but laid siege to the Shakhtar goal during the first 15 minutes, Roma undeservedly fell behind.
Brazilian Willian surged down the left before checking his run and delivering an inswinging low cross which Hubschman, at the near post, flicked in with the faintest contact.
The Italian side now needed three goals. Rodrigo Taddei should have got the first but he mistimed his volley horribly from David Pizarro's corner.
If that attempt was embarrassing, Roma's next was shameful.
Shakhtar's Mkhitaryan, in an attempt to stop Borriello from getting his strike away, hauled down the Italian and conceded a penalty.
The forward took on the responsibility from the spot but struck his effort straight at the Shakhtar keeper.
The visitors still had enough time on their hands but they were dealt a further blow four minutes before the interval when Mexes received a second booking for pulling back Adriano on the halfway line.
They were lucky to retain 10 men on the pitch when Daniele De Rossi appeared to thrust his arm into the face of Shakhtar captain Darijo Srna. English referee Howard Webb missed the incident and instead booked Srna for complaining.
Roma, seemingly shell-shocked from events in the first half, failed to trouble Pyatov after the break, while the home side began to control the match.
Armenian Mkhitaryan was an impressive attacking outlet all night and his delivery from a corner led to Shakhtar's second which was curled in brilliantly by Willian to make it 5-2 on aggregate.
Former Arsenal striker Eduardo was then brought on to the field of play and he added the finishing touch to a historic night for the Ukraine side by taking advantage of Aleandro Rosi's poor back pass to slot in a third.
Shakhtar boss Mircea Lucescu: "We played much better than they did. Of course, 11 against 10 is easier.
"They were nervous and made a lot of mistakes and we knew how to control the situation."
Roma caretaker coach Vincenzo Montella: "We have to develop the ideas and the pace that I saw in the first 30 minutes of the game.
"I tried to keep up the competitive spirit of the team despite the nervous atmosphere after Mexes was sent off. We will analyse our mistakes and move forward."
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