Renato laid on the opener for Fabiano just before the break and midway through the second half Fabiano's header was glanced in by Renato.
The Romanian champions, managed by former Chelsea midfielder Dan Petrescu, were well organised in defence and restricted their hosts to few sights of goal in the first half, despite Sevilla dominating possession.
Fabiano stung keeper Giedrius Arlauskis's hands with a free kick and had another close-range shot saved.
Unirea were undone in the last move of the half. Renato broke down the left and pulled his cross back to the edge of the area, from where Fabiano finished with a first-time shot into the corner.
"Sevilla have some great players and I believe that today I have seen the best striker in the world in Luis Fabiano," said Petrescu. "I haven't seen a player do what he can do in a long time."
There was little change after the restart until the 70th minute.
Substitute Alvaro Negredo had just had a shot saved when Fabiano's header from a corner was nodded in by Renato at the far post.
Having been sturdy in defence, Unirea offered little going forward as they were forced to open up and chase the game.
Renato almost made it 3-0 at the end when his fine left-foot volley came back off the base of the post.
"It was a question of being patient and moving the ball around," said Sevilla coach Manolo Jimenez. "They played a good game and I want to congratulate them on their defence which made it very difficult until we scored the first goal."
