The win, Unirea's first at home in European competition, put the Romanians onto eight points in Group G, two more than third-placed Stuttgart. The two sides meet in Germany in the final group game on December 9 with Unirea needing a point to progress.
Sevilla, who had already qualified and have 10 points, dominated the opening half with strikers Frederic Kanoute and Alvaro Negredo both hitting the post.
"We are extremely happy, we did not manage a spectacular game but we have managed to win," Unirea defender George Galamaz told public television TVR 1.
"I don't know what happened to us."
The second half was more balanced, but Unirea midfielder Dacian Varga missed three great opportunities to score while Sevilla could not break down the Romanian team's well-organised defence.
"When you win against a team like Sevilla and you have eight points, you would like to have been already qualified," Petrescu told TVR 1.
"But I guess every match in this competition has to be the match of our lives. You get tired at some point."
