Roma progressed to the Champions League knockout stage as Group C winners after beating Qarabag 1-0 on Tuesday.
Diego Perotti scored early in the second half and Roma finished top of the group after Atletico Madrid drew at already-qualified Chelsea 1-1 in the other match.
The match in England still had a couple of more minutes to go after the final whistle in Rome. All of the Roma squad waited in front of their fans and, as soon as the big screen showed it was over, there were huge cheers from players and supporters.
"It's a wonderful moment for us," Perotti said. "When the draw was made, nobody believed in us, but we worked hard and we deserved this first place.
"t was difficult. They were all behind the ball, it seemed as if they had something to play for. We were patient. These games are more dangerous and we didn't lose our heads, fighting together for the goal. Now we're going to enjoy it."
Roma knew they needed a victory against the group minnows to reach the round of 16 or hope Atletico failed to win at Stamford Bridge.
Qarabag finished bottom of the group after earning two points from a pair of draws with Atletico Madrid.
The Italian side attacked from the start but found it hard to create decent goal scoring opportunities.
Their best chance of the first period came in stoppage time as first Edin Dzeko fired over before Radja Nainggolan saw his effort well saved by Ibrahim Sehic, who also kept out Aleksandar Kolarov's follow-up.
Roma broke the deadlock eight minutes after the break. Sehic kept out Dzeko's effort with his knee, but the ball looped up and Perotti headed it into the back of the net.
Sehic pulled off another good save to deny Nainggolan as Roma sought the second goal which would have sealed the victory.
Qarabag almost levelled seven minutes from time when Wilde Donald Guerrier crossed for an unmarked Michel but he headed straight at Roma goalkeeper Alisson.