A 1-0 win, after a 2-1 defeat in Kharkiv, took Roma through on away goals as Dzeko scored seven minutes into the second half with the game's first chance of note.
Having trailed 2-1 from the first leg, Roma looked bereft of ideas for much of the contest at the Stadio Olimpico before Dzeko broke the deadlock in the 52nd minute following a tepid first half devoid of goal-mouth action.
Dzeko also curled a shot from the edge of the penalty area inches wide in the 62nd minute before Shakhtar centre back Ordets was shown a straight red card in the 79th for hauling down the Bosnian when he was through on goal.
Eusebio Di Francesco's side is the second Italian team to advance to the quarter-finals after Juventus, with the draw for the last eight taking place on Friday.
Manchester United had David de Gea to thank for a battling 0-0 draw in Sevilla, but will be hoping to spend more time on the front foot at Old Trafford.
The Spanish outfit progressed to the quarter-finals for the first time in their history, with goals from substitute Wissam Ben Yedder in the 74th and 78th minutes.
Buveur d'Air Claims The Champions Hurdle At Cheltenham
The concluding Close Brothers Novices' Handicap Chase went to Mick Channon's 13-2 shot Mister Whitaker, ridden by Brian Hughes. Last seen winning the Tolworth at Sandown, he quickened up well to deny Amy Murphy's Kalashnikov in the final few strides.
While that was the signature event in these characters' lives, Tuesday's episode served notice that life goes on. We decided we wanted something that was sort of vintage in its own way, but very classic, but still contemporary.
Let's not exactly say, "At least they're doing this now", but simply, as a matter of fact, "They're doing this now". Mason also uncovered a string of oddities-photos of "the native person fascinated by Western technology.
Klopp picked out counter-pressing, good decision making and fantastic attitude as being vital for Liverpool at Old Trafford. Big rivalry for ages but in the last few years Man United were more successful than us, we respect that.
According to reports, Patriots running back Dion Lewis will sign a multi-year deal with the New England Patriots . NFL Network's Ian Rapoport reported Lewis' contract will make him one of the 10 highest paid running backs.
A Pro Bowler in 2015 and twice a second-team All-Pro, Wilkerson will help strengthen the Packers' front-seven. The Packers won the race for Wilkerson's service. "#Packers should be getting a motivated player".
New Development Bank and International Solar Alliance have joined hands to promote solar energy across the globe. He said the member countries of the ISA would ensure distribution of finance and expertise.
The actress, 56 years old, was arrested, hospitalized and placed in police custody after being beaten with his may. Domestic violence charges against her boyfriend were dropped but four misdemeanour counts of battery were upheld.
The players asked the woman for her name - she refused to identify herself - instead, babbling and cussing away. There's a lot of cross-talk, but it's clear the players are more bemused by the ranting woman than bothered.
He served in active duty from May 2010 to August 2013 and was deployed to Afghanistan from April 2011 to March 2012. Jerry Brown had offered the state's employee assistance program, which had already sent counsellors to the campus.
Geofencing Market Size & Share poised for growth
Market Size Forecast: Global Overall Size, By Type/Product Category, By Applications/End Users, By Regions/Geography. After a brief overview of the Global Smart Airports market , the report analyzes the market dynamics.
JUST KIDDING: Selma Blair says Cameron Diaz not retired
Despite having a successful career, the actor suddenly stopping acting and she also seems to have no projects in the pipeline. However, Selma has since backtracked on her comments after the news hit headlines all over the world yesterday.
New York Jets, Teddy Bridgewater Working On Deal
Bridgewater, meanwhile, is gradually working his way back from a serious knee injury that cost him most of the past two seasons. That changed in August 2016, however, after a devastating knee injury put his National Football League future in jeopardy.