Visitors Sevilla twice struck the woodwork in the opening 20 minutes, with striker Fredi Kanoute hitting the post from six yards and Alvaro Negredo heading against the bar, before Dragutinovic's misplaced header handed Unirea a half-time lead.Dacian Varga had three good opportunities to extend that advantage in the second period, but the second-placed Romanians had to be content with the solitary goal.
They meet Stuttgart - 2-0 winners over Rangers - in the final group game next month as they bid to join Sevilla in the knockout stages.
Already-qualified Sevilla were urged to go for three points in order to make sure of top spot in Group G by club president Jose Maria del Nido, having booked their place in the last 16 with a 1-1 home draw against Stuttgart three weeks ago.
The Andalusians began the match five points clear of Unirea and made a determined start. Kanoute struck the upright after eight minutes, drilling a right-foot volley off the post from six yards before Jesus Navas forced Giedrius Arlauskis into a save from 12 yards.
Javi Varas held a free-kick from Valeriu Bordeanu at the other end before Negredo shot over and then headed against the crossbar from 12 yards.
Arlauskis saved from Navas and Kanoute shot wide before Diego Capel had a shot blocked as Sevilla continued to have the better of proceedings.
Varas saved a Ricardo Gomes effort before Unirea took the lead moments before the interval.
Abdoulay Konko's foul on Sorin Frunza earned Unirea a free-kick in a dangerous position and Ersin Mehmedovic delivered the ball into the area where, under no pressure, Dragutinovic headed into the bottom-left corner from 12 yards.
Unirea made a strong start to the second half, with Varga cutting inside to the left of the penalty area for a right-foot shot which Varas could only parry.
After 61 minutes, Varga again had an opportunity to extend Unirea's lead, only to drag his left-foot shot wide from six yards.
Navas shot wide with a 25-yard right-foot effort at the other end before Varga again missed the target, firing over from the right side of the penalty area.
Arlauskis parried a Diego Perotti shot from 12 yards as Sevilla again tested the Unirea goalkeeper before Konko struck a free-kick against the defensive wall.
Sevilla attempted to preserve their unbeaten run in the latter stages, pressing forward in stoppage time.
But the closest they came was when Navas' shot dropped for Konko in the second minute of additional time and his right-foot effort from the centre of penalty area was tipped over by Arlauskis.
Unirea Urziceni 1 - 0 Sevilla FC
