The visitors suffered a big blow ten minutes before time as Ivan Ordets was sent off after pulling down Dzeko who was clear on goal. "Among the eight best sides in Europe and we push onto the next round".
It took Dzeko just 22 seconds to work Andriy Pyatov for the first time, but Shakhtar would not bow easily to the hosts' early pressure and were soon knocking the ball around with confidence in the Roma half.
The two teams went into the interval level, with the visitors looking the more risky of the two in the opening stages.
"[Paulo] Fonseca's team has technical and fast players who can find space between the lines and as soon as you give them space on the pitch they turn around and counter-attack you, which is what happened in the second half".
"We made a few too many mistakes in the first leg and they made the majority". "Shakhtar dominated the entire game and were always around the Roma area, even when going down to 10 men against 11".
But Dzeko rescued the Italian giants with a strike after 52 minutes to bring their quarter final hopes back to life.
The 31-year-old striker kept his composure and delicately guided the ball into the back of the net with the outside of his right foot, swinging the pendulum in Roma's favour through away goals.
'Roma have had the satisfaction this year, despite some hard times, of getting into the quarter-finals of the UEFA Champions League and we need to be proud of this.
The champions of Ukraine went for broke in the final five minutes of the match, knowing an equaliser would send them through to the last eight, but the Eternal City outfit held on for a narrow victory.
15 - Manchester United haven't managed to score more than one goal in any of their last 15 Champions League encounters with Spanish opposition (seven goals in total). "I don't have a preferred opponent: they are all strong teams, but we will play to win against anyone".