Bruno Fernandes and Edinson Cavani both struck twice as the Red Devils produced a stunning turnaround.
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Manchester United scored five second-half goals to take a giant step towards the UEFA Europa League final.
Match in brief
Roma endured a terrible first ten minutes with Jordan Veretout forced off injured before Bruno Fernandes clipped in the opening goal from Edinson Cavani's adroit pass. Paulo Fonseca's men regrouped, however, and quickly restored parity through Lorenzo Pellegrini's penalty after Paul Pogba handballed.
The Giallorossi also lost goalkeeper Pau López and Leonardo Spinazzola to injuries before the break yet, in between, took the lead when Pellegrini slid in a low cross for Edin Džeko to bury.
It was a different story after half-time as United found their brilliant best, with Cavani spearheading the turnaround. The Uruguayan struck twice to make it 3-2, with a Bruno Fernandes penalty, Pogba header and Mason Greenwood finish giving Ole Gunnar Solskjær's men a commanding advantage going into the return.
Matthew Howarth, Man. United reporter
United took a while to regain their composure after falling behind but emerged for the second half with renewed purpose – and got their just rewards. Roma's two away goals give them a glimmer of hope going into next week's return leg, but the Red Devils' four-goal cushion leaves them in a tremendous position to end their semi-final hoodoo under Solskjær.
Vieri Capretta, Roma reporter
The Giallorossi reacted well to the hosts' opener and had a game plan that worked in the first half – solid at the back and quick on the break. Some sloppy defending in the second half, mixed with the inability to counter, meant United had it easy. Roma know how to produce an epic comeback at the Olimpico (ask Barcelona), so don't consider them finished just yet, though scoring four goals seems frankly near to the impossible.
Paul Pogba, Man. United midfielder: "The result is positive, but it's not finished. In the first half, we made two mistakes and conceded two goals. When we conceded the second, we were a bit all over the place. At half-time, we said, 'Let's do the right things, let's do the simple things.' We were all motivated and determined to go and score as many goals as possible."
Ole Gunnar Solskjær, Man. United manager: "We took most of our chances today, so we're very pleased. The character showed – we came back, we didn't lose our heads. For five, ten minutes at the end of the first half we didn't look great, but we got it together."
Paulo Fonseca, Roma coach: "It's difficult to explain how the same team that did so well in the first half had that kind of second half. It's hard to play against a side like United without having the substitutions. It's positive to reach this stage of the competition anyway, and also to play like we did in the first half. But in the second half we got everything wrong."
- The total of eight goals matched the record for goals scored in a single UEFA Europa League game.
- United have not lost at home in a European semi-final since April 1997, winning five and drawing three games since.
- Bruno Fernandes has scored 20 of his 21 penalties taken for Manchester United in all competitions.
- Roma are the first team to make three substitutions in the first half of a UEFA Europa League match.
- Edin Džeko has scored six goals in his last five appearances against United at Old Trafford.
Manchester United: De Gea; Wan-Bissaka, Lindelöf, Maguire, Shaw; McTominay, Fred (Matić 83); Rashford (Greenwood 76), Bruno Fernandes (Mata 89), Pogba; Cavani
Roma: Pau López (Mirante 28); Smalling, Cristante, Ibañez; Karsdorp, Diawara, Veretout (Villar 5), Spinazzola (Bruno Peres 37); Pellegrini, Mkhitaryan; Džeko
The second leg takes place in Rome next Thursday, but before then there are league games on Sunday: Manchester United host Liverpool while Roma travel to Sampdoria in Serie A.