Lee McCulloch thought he had secured the win with a superb strike with just 11 minutes to go but Unirea hit back to claim a point when substitute Marius Onofras grabbed a last-gasp leveller.
The biggest surprise in Walter Smith's team selection was the decision to hand 17-year-old Danny Wilson his first taste of Champions League action alongside David Weir in the heart of defence, while McCulloch was also drafted straight into the side after recovering from injury.
Unirea goalkeeper Giedrius Arlauskis missed their win in Glasgow through injury but returned to reclaim the gloves from Daniel Tudor, while Bruno Fernandes missed out with a thigh strain.
The Romanians looked the more dangerous in the opening spell and Tiberiu Balan should have done better when he found himself with a chance at goal early on but his shot was weak and easily dealt with by Allan McGregor.
Sorin Frunza then whipped a decent ball into the box intended for Balan in front of goal but Wilson was able to intercept and punt the ball out of play for a corner, with the home side failing to capitalise on the flag-kick.
Rangers had an opportunity to put their hosts under pressure when Kevin Thomson was fouled 25 yards out. He stepped up for the set-piece himself and his well-struck curling effort was spilled by Arlauskis but the Unirea defence were able to clear the danger.
The Scottish champions were threatening again when a long ball from Steven Whittaker found Steven Naismith at the back post and he nodded narrowly wide of the goalkeeper's right-hand upright.
Arlauskis was called into action to block from Thomson again, before Naismith followed up with a header that the keeper also managed to keep out as Rangers attempted to crank up the pressure.
Kyle Lafferty picked up the first booking of the game for a foolish challenge on Serban Varga, before Vasile Maftei tested McGregor with a stinging shot from distance that he managed to push past the post.
The Rangers goalkeeper then pulled off a superb one-handed save to keep the scoreline level when he swatted Frunza's shot to safety at full stretch after the midfielder had pounced on Varga's cut-back.
At the other end, Lafferty saw his shot flash across the face of goal and wide as the first half ended goalless.
There was trouble at half-time when a section of the Rangers support clashed with stewards and missiles appeared to be thrown in the section housing around 2,000 away fans.
An announcement was then made over the PA system warning that the game would be suspended if the violence did not stop and, by the time the second half was under way, the situation had calmed down.
Back on the pitch, Unirea stepped up their efforts to open the scoring and the impressive Frunza was causing problems again when he unleashed a 25-yard drive which was smothered by McGregor.
Rangers then had a great chance of their own when Steven Davis slipped a pass through for Kenny Miller and he managed to beat the offside trap but the finish was poor and Arlauskis was able to gather.
McGregor had been in fine form all night and he came to the rescue of Rangers again, this time to deny Onofras at the near post, before blocking from a Marius Bilasco volley.
It was Rangers who stunned the home side when they opened the scoring with 79 minutes gone when McCulloch tried his luck with an audacious long-range shot which fizzed past the helpless Arlauskis and into the back of the net.
Wilson had impressed on his debut and had a crucial part to play when he nodded Onofras' effort off the line as Unirea came agonisingly close to equalising just moments later.
But Unirea were celebrating with just two minutes to go when Onofras rifled into the top corner of the net from distance as Rangers were forced to settle for a point.