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The Giallorossi will take a commanding lead into next week's second leg in Kiev, as they look to move on to the quarter-finals of this season's Europa League.
And that is down in no small part to El Shaarawy, who came off the bench to score his first goal since returning to the club - and in the process put Paulo Fonseca's side in control of the tie.
They already had the lead at the Stadio Olimpico by that point - and courtesy of another Italy international, Lorenzo Pellegrini, too. The captain latched onto Pedro's clever through-ball before expertly steering home his shot; a vital first salvo in the tie.
Shakhtar had their chances during the course of the contest - they dominated possession, and Pau Lopez made at least one world-class save to prevent them grabbing an away goal - but they were left in a tricky position after Gianluca Mancini headed home a third for the hosts with just under 15 minutes remaining.
With the game finishing like that, Fonseca knows that if his side manage one goal in Kiev their opponents will have to score five to prevent them progressing.
There is still a week before that fixture, however. Prior to that, the Giallorossi travel to face relegation-threatened Parma on Sunday afternoon.
ROMA 3-0 SHAKHTAR DONETSK
SCORERS: Pellegrini (23'), El Shaarawy (73'), Mancini (77')
ROMA (3-4-2-1): Pau Lopez; Mancini, Cristante, Kumbulla; Karsdorp, Diawara (Ibanez), Villar, Spinazzola (Peres); Pellegrini (Perez), Pedro (El Shaarawy); Mkhitaryan (Mayoral)
Unused subs: Mirante, Fuzato, Smalling, Dzeko, Santon, Calafiori
SHAKHTAR DONETSK (4-2-3-1): Trubin; Dodo, Vitao, Matvienko, Ismaily; Maycon, Alan Patrick (Solomon); Marlos (Marcos Antonio); Tete (Konoplyanka), Moraes (Dentinho), Taison (Sudakov)
Unused subs: Shevchenko, Pytatov, Kryvtsov, Kornilenko, Bolbat, V’Yunnik, Bondar
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