Their hopes of progress were already likely to hinge on their trip to Naples later this month but now they have a two-point advantage over the Italians, victory will make certain.
After victory at Villarreal, Mancini said: "I think this win is important because now we have a good chance.
"We know that everything will be in Naples.
"I think it will be an incredible atmosphere. There will be 70,000 people at the stadium.
"I think it is very difficult to play but it is important to go there with this result.
"I don't think it was easy to win here but we played very well and after the first goal it was easier. That was really important."