Edin Dzeko now has four goals in the Champions League this season
Edin Dzeko's strike ensured Roma reached the Champions League quarter-finals for the first time since 2008 with victory over Shakhtar Donetsk.
The former Manchester City forward latched on to Kevin Strootman's through ball before poking the ball between Andriy Pyatov's legs for the only goal.
The Italians, who lost the first leg 2-1, went through on away goals.
Ukrainians Shakhtar had Ivan Ordets sent off after he pulled Dzeko down by the shirt.
Shakhtar were unlucky not to get an away goal of their own early on when Roma's Alessandro Florenzi almost headed an in-swinging free-kick into his own net with a glancing clearance.
But Roma quickly started to find their rhythm and Shakhtar goalkeeper Pyatov had to react quickly to a low Aleksandar Kolorov cross, palming the ball away from the path of the incoming Dzeko.
A mistake from Federico Fazio saw Facundo Ferreyra go clear on goal, but the Argentine defender was able to recover in time to put his opponent off - his shot going well wide of Alisson Becker's post.
Just a minute later, Shakhtar broke from a Roma corner, with Florenzi forced into a perfectly timed clearing tackle on Ismaily inside the area.
Roma finally broke the deadlock after the break, with Bosnian Dzeko beating the offside trap to score past Pyatov.
He could have had a second just after the hour mark when he curled in an effort from outside the area but it sailed inches wide of the top left-hand corner.
Ordets was shown a red card for tugging on Dzeko's shirt, before a scuffle broke out on the pitch after two Shakhtar players pushed a ballboy over the advertising boards for holding on to the ball.
'A single moment' - What they said
Roma players celebrate Edin Dzeko's second-half goal
Roma goalscorer Edin Dzeko: "The standing ovation is not for me but for everyone - we are deservedly in the quarter-finals.
"We managed to do something Roma hadn't in 10 years, so going forward to play against the best makes us all very proud.
"We are among the eight best sides in Europe."
Roma boss Eusebio di Francesco: "We knew that sooner or later they would make a mistake and we'd pounce on it.
"If we face any opponent with this attitude and determination, we can go far."
Shakhtar Donetsk manager Paulo Fonseca: "Roma made the most of a single moment.
"Dzeko of course was a key player, but apart from his goal they didn't have a chance, we had possession.
"If we had finished off the chances we had in the first leg the match would already have been over."
-- Courtesy of BBC Sport