Cengiz Under's away goal looms large, but Facundo Ferreyra and Fred struck in the second half to tilt the balance to Shakhtar, which went on to rout its next two opponents in the league by a combined 8-0 score.
Ukrainian side Shakhtar saw their 2-1 first-leg lead cancelled out by Edin Dzeko's strike as Roma reached the last eight for the first time in 10 years via the away goal rule. The incident led to a scuffle on the pitch, but Ferreyra was not penalized for his actions.
The key point of the fight occurred in the 52nd minute - Dzeko, taking advantage of a positional mistake Ordets, broke out bore down on goal and beat the goalkeeper of the national team of Ukraine.
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"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.
UEFA says it charged Roma for timewasting by a ballboy during its Champions League win over Shakhtar Donetsk.
After Italy's shock failure to qualify for the World Cup, Roma's progress to the last eight along with Juventus is a boost for the country.
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Despite being a man down, Shakhtar launched a late onslaught and had several risky raids down the left but the home team's defence held on until the final whistle.
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.
The Daily Mail recently reported that Fonseca is Farhad Moshiri's top target to replace Sam Allardyce as Everton manager this summer, and Toffees fans unsurprisingly had comments to make after Shakhtar's exit.
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I'm all down for experience - not against it whatsoever - but I've never been there before". But it's nice to know that even millionaire supermodels make drunken errors sometime.