Shakhtar went into the game looking to reach the quarter-finals of the Champions League for the first time since the 2010/11 season (when they qualified at the expense of Roma) but they left the Italian capital empty-handed this time.
The game ebbed and flowed but was generally very evenly-matched throughout.
Edin Dzeko had his first sight of goal with barely a minute of the clock as he fired straight at Andriy Pyatov after being fed by Radja Nainggolan.
The visitors were the next to threaten though as Alessandro Florenzi was just inches away from heading a free-kick into the back of his own net.
Whilst there was plenty of tempo to the game in the first half gilt-edged chances were at a premium.
Taison fired over Alisson's crossbar from range, whilst Facundo Ferreyra failed to punish Federico Fazio's mistake at the back as he could only find the side-netting.
Diego Perotti saw an effort flash just wide from the edge of the box just before the break as the two sides went in goalless at the half.
However, Dzeko ensured that the game would not end goalless just seven minutes into the second period, racing clear and prodding past Pyatov after a fine ball from Kevin Strootman.
13 de marzo de 2018
That goal gave Roma a boost and now aware that they were behind in the tie, Shakhtar began to take more risks, opening up more opportunities for the hosts on the counter.
Perotti fired straight at Pyatov from the edge of the box, before Dzeko was inches away from a second of the night when his first-time effort following a cutback from the right dropped narrowly wide of the far post.
The Bosnian should have done better with 67 minutes gone as he was played in on the counter by Perotti but he lost his footing at the key moment and contrived to blaze the ball harmlessly over the bar.
With just 11 minutes to go, Shakhtar's hopes of progressing were all but ended when defender Ivan Ordets was given his marching orders for bringing down Dzeko, leaving the visitors a man down as they searched for the goal they so desperately needed.
Despite some heavy late pressure that goal never came as Roma held out to qualify for the last eight for only the fourth time in the club's history.
13 de marzo de 2018