Roma, beyond the round of 16 for the first time since 2008, advanced on away goals after losing 2-1 in the first leg in Ukraine on Feb. 21.

Dzeko, who had his first chance in the opening minute, broke Shakhtar's stout back four in the 52nd. Kevin Strootman beat the offside trap with a through ball that Dzeko collected just inside the penalty area on the left, and with Andriy Pyatov out to play it, Dzeko calmly finished between the goalkeeper's legs from 16 yards.

The Bosnia international nearly doubled the lead seven minutes later on a feed from Radja Nainggolan, but his attempt at the top-left corner went wide.

Shakhtar, who controlled possession throughout the first half, went down a man in the 79th minute when Ivan Ordets was shown a straight red card for taking down Dzeko from behind just outside the penalty area.

The resulting dispute led to several skirmishes among players on both sides, culminating in a bizarre scene in which a ballboy was pushed over the advertising hoarding by a Shakhtar player.

That loss of focus contributed to a hectic final 10 minutes plus four minutes of added time for the visitors, whose only remaining chance was from a free kick in the 88th minute that was quickly snuffed out.

Shakhtar, seeking to move on to the quarterfinals for the first time since they knocked Roma out in the round of 16 in 2011, have still never won in a European competition in Italy in nine chances.

And with the clean sheet, Roma goalkeeper Alisson has yet to concede at the Stade Olimpico in the Champions League this season.