Unirea, the team from rural Romania whose stadium holds just 7,000 fans, recorded their first win in European competition having scored their first away goals to demolish a hapless Rangers side who led through a Ricardo Vilana own goal.
Second-half own goals by Kyle Lafferty and Lee McCulloch put the visitors 3-1 ahead after Marius Bilasco had equalised and Rangers' Steven Davis missed a penalty before the break.
Pablo Brandan drove home a low shot to make it 4-1 and wrap up the points for Unirea who now have four from three games. Rangers have one point and are bottom of the group.
"I believe in the second half we had a bit of luck," Unirea manager Dan Petrescu told reporters.
"We scored the second goal from a deflection and that made it easy for us, but my players also made it look easy. Before that we didn't play well."
The early Rangers goal, which came after a fierce Pedro Mendes shot hit Vilana and deflected over keeper Daniel Tudor, stunned the Romanians and Petrescu said: "I never expected a goal in the second minute (from them) and I had to take action immediately. I could not afford to lose and we took a risk and we won."
Unirea pulled level with a simple equaliser as Brandan charged into the area on the left before driving a low ball across the face of goal for the unmarked Bilasco to score.
Rangers then wasted a great chance to score when Tudor saved Davis's spot kick on 38 minutes and their anguish was compounded just four minutes into the second period when a shot from Bruno Fernandes clipped substitute Lafferty and flew beyond keeper Allan McGregor.
Unirea made it 3-1 just before the hour as Tiberiu Balan's deep free-kick from the left was headed into his own net at the near post by McCulloch. Six minutes later Brandan drove a low shot into the bottom left for their fourth goal.
"That type of defending at any level is not good enough," said disappointed Rangers manager Walter Smith.
