The first meeting with the score 2:1 won the champion of Ukraine.
Mallenco twice worked for the matches of Shakhtar in the Champions League in the 2014-2015 season, "miners" in the 1/8 finals of painted draw with Bayern (0:0), and in the autumn of a year ago thanks to the double beat Bernard "Feyenoord" (2:1).
Shakhtar had defender Ivan Ordets sent off on 79 minutes after he brought down goalscorer Dzeko and Paulo Fonseca's side very quickly could have gone down to nine men with Ferreyra sparking an all-out brawl following his sideline scuffle.
The Champions League round of 16 completes on Wednesday, and the draw for the quarterfinal round will take place on Friday, with no restrictions placed on which teams can be paired together. "We are among the eight strongest teams in Europe, it means we are strong too".More news: This Is Us season 2 finale recap: 'The Wedding'
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They survived a scare at the other end on 10 minutes, however, when Alessandro Florenzi diverted a free-kick just wide of his own goal with an attempted clearing header.
But Roma came back from the break with renewed intensity and Dzeko scored in the 51st minute to bring the sides level at 2-2.
"What I liked best is that we played like men and that's the most important thing if we want to aspire to certain goals and dreams", said Roma coach Eusebio Di Francesco, in his first ever Champions League campaign.
Dzeko then looked to turn provider with an exquisite through-ball for Gerson on 73 minutes, but the Brazilian failed to test Pyatov with a poor strike from inside the box.
Scenes at full time as Roma reach #UCL quarter-finals for the first time since 2008.
"The standing ovation is not for me but for everyone, we are deservedly in the quarter-finals", said Dzeko of the applause which accompanied him off the pitch.