Cengiz Under's goal and a string of Alisson saves in a 2-1 away first-leg defeat had kept Roma in the tie, and Eusebio Di Francesco's men edged to victory in the return to reach the quarter-finals despite a dismal display in which Dzeko's victor was scarcely deserved.
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.
Shakhtar's chances of producing a comeback were dealt a huge blow in the 79 minute when they were reduced to 10 men following the sending off of Ivan Ordets after straight red card.
"We are among the eight best sides in Europe, so that means we're strong too".
Eagles starting to benefit from 'title chasers,' cut Brent Celek
Philly drafted him in the fifth round in 2007 and spent his entire 11-year National Football League career with the team. The 6-4, 255-pound tight end caught 398 passes for 4,998 yards and 31 touchdowns during his career with the Eagles.
The 31-year-old has now been directly involved in six of Roma's Champions League goals this season.
Ferreyra then came close after Federico Fazio lost the ball just outside his own box, before Roma struck seven minutes into the second half.
Neither side could find the breakthrough by half time, but the Giallorossi went on to take the lead not long after the restart when Dzeko sprung the offside trap to latch on to a Kevin Strootman through-ball. "We deserve to go through, to be in the quarter-finals".
"Roma made the most of a single moment", said Shakhtar coach Paulo Fonseca.
Watch Iris Suit Up As A Speedster On The Flash
Fans will remember seeing Jessica Parker Kennedy's mystery waitress brief interaction with Barry Allen moments before his wedding. Since then, she's appeared twice on The Flash , each in a scene where she has an awkward encounter with members of Team Flash .
The Bosnian striker scored the only goal of the second leg to put the Serie A side through on away goals against Shakhtar.
Despite being a man down Shakhtar pushed forward in search of the goal that would send them into the quarterfinals of the competition but they were unable to do so, losing 1-0 on the night and exiting the Champions League on the away goals after a 2-2 aggregate scoreline. - This is the first time Roma have progressed from a knockout tie in which they have lost the first leg; ending a run of five consecutive knockout tie defeats.
Antonio Conte could make that four with his Chelsea side face Barcelona on Wednesday.
Waiting Game: Browns Still Not Sure Of Joe Thomas' Future
Browns star tackle Joe Thomas has not informed the team of his future plans as Cleveland prepares to sign free agents. It was just past year that Cleveland made Kevin Zeitler the highest-paid guard in National Football League history.