Shakhtar go through after emphatic win over Roma
Roma had gone into the match in buoyant mood under new manager Vincenzo Montella but the game was virtually over when, trailing 1-0, they were reduced to 10 men just before halftime when Philippe Mexes was sent off for a second yellow card.
The Italians were already ruing a missed chance after striker Marco Borriello fluffed a 28th-minute penalty.
The win made Shakhtar the first Ukrainian side to get to the Champions League last eight since Dynamo Kiev who reached the semi-finals in 1999.
Tomas Hubschman set Shakhtar, five-times Ukrainian champions, on the way to victory with a neat back flick from a cross by Willian in the 18th minute.
The 22-year-old Brazilian scored himself after the break, side-stepping David Pizarro and curling a shot in off the post.
Striker Eduardo scored the third in the 87th minute to complete the drubbing.
Borriello, the most dangerous man on the pitch for much of the game, had looked full of confidence as he ran up to take the first-half spot kick but he struck the ball weakly and Shakhtar goalkeeper Andriy Pyatov bundled it round the post.
British referee Howard Webb had no hesitation giving Mexes, Roma’s central defender, a second yellow card for a clumsy foul on Luiz Adriano, reducing Roma to 10 men for the second half.