Luiz Adriano nets Shakhtar's third goal in the first half.
Knockout round debutants Shakhtar Donetsk are in the box seat to make the Champions League quarter-finals after recording a 3-2 away win against Roma on Wednesday.
Roma took the lead in the 28th minute when midfielder Simone Perrotta headed in a cross from Rodrigo Taddei off Razvan Rat, but fans had little time to savour the goal as Shakhtar equalised a minute later through Jadson's fortunate deflection.
The Ukrainians, who looked fresh despite not having played a competitive match in more than two months, then seized control of the match with a lovely curling shot from just outside the area by Douglas Costa on 36 minutes.
Luiz Adriano slotted in the visitors' third before half-time, capitalising on a slip-up by Roma defender John Arne Riise that summed up their frustrating evening, before Jeremy Menez superbly netted for the hosts after the break.
Claudio Ranieri's side will have their work cut out to win in Ukraine, with Skakhtar unbeaten in their last 53 matches in all competitions at home. Their last loss at the Donbass Arena came in October 2008.
After successive Serie A defeats to Napoli and Inter Milan, Ranieri's side came out firing and dominated the early stages of the contest.
Nicolas Burdisso and Mirko Vucinic went close to scoring before Roma took a deserved lead through Perotta.
Jadson's right-footed equalizer from 18 yards took a wicked deflection of Daniele De Rossi, leaving Roma goalkeeper Doni stranded.
The goal spurred Shakhtar on and Jadson was again involved when the Ukraine side scored its second, finding countryman Douglas Costa who hit a curling left-foot strike from the edge of the area.
Things got even worse for Roma on 41 minutes when left-back Jon Arne Riise slipped on the touchline while he had the ball.
Riise's mistake allowed Douglas Costa to steal the ball, and the Brazilian took his time before picking out compatriot Luiz Adriano to sidefoot into the back of the net.
The goal capped a horrendous spell for Roma and the hosts certainly knew what the crowd thought of their performance, with Ranieri's men booed by the Stadio Olimpico fans as they entered the field for the second half.
But as they did in the first half, Roma began strongly and Frenchman Jeremy Menez scored a splendid goal to bring his side back into contention just after the hour mark.
Menez beat Jadson for the ball in a show of strength before streaming forward and producing a sensational strike into the top right corner from 25 yards.
Shakhtar continued to search for a fourth as Luiz Adriano and Henrikh Mkhitaryan went close, while Roma also had a chance to score but Andriy Pyatov kept out Francesco Totti's late effort.
