Edinson Cavani scored both United goals in the second leg of a 13-goal semi-final.
The Uruguayan opened the scoring with a fabulous first-half effort, then found the net with a fine header from Bruno Fernandes’ excellent floated pass in the second half.
In between, Roma briefly threatened a comeback when former Manchester City forward Edin Dzeko scored his ninth goal against United before Bryan Cristante finished smartly with a shot on the turn.
The Italians had the final word when Nicola Zalewski’s low drive went in through David de Gea’s legs after taking a deflection off Alex Telles.
United are without a trophy since their last triumph in this competition in 2017, their longest run since the five-year gap between 1985 and 1990, which was ended by an FA Cup success that marked the start of Sir Alex Ferguson’s silverware collection.
Cavani is developing into United’s talisman
If getting to within one win of a trophy as United manager was a triumph for Solskjaer, it also underlined why the Norwegian is persisting in his efforts to keep Cavani at Old Trafford.
At 19, Mason Greenwood is at the other end of the age scale to Cavani. The England man eclipsed Duncan Edwards as the youngest Englishman to reach 100 appearances for United, and the third youngest ever behind Norman Whiteside and George Best.
Evidently, Greenwood has much to learn. Cavani, 34, is the finished article.
His four goals in the tie have taken him to 14 for the season and a run of seven goals in six games suggests he is reaching top form at just the right time.
Cavani’s first-half effort was stunning. Starting with Paul Pogba winning possession, United’s team work was brilliant. A fantastic lay-off by Fernandes sent Fred running through midfield. The pass was good but Cavani still had work to do as he belted his shot into the Roma net.
His second was more subtle, coming from another Fernandes assist – a deep cross delivered to perfection, which invited the headed finish which effectively killed the tie.
The word is Cavani is now minded to stay at United for another season and as by far the best orthodox number nine at his disposal, Solskjaer will be delighted if those suggestions prove to be correct.