After taking the lead through a deflected Pedro Mendes goal within 60 seconds things just seemed to go from bad to worse.
Marius Bilasco equalised on 32 minutes although the ease in which Pablo Brandon found space to pick his cross from the left had alarm bells ringing.
Rangers, however, had the perfect opportunity to regain their lead before the break but Steven Davis was guilty of missing a penalty; it was a moment that changed the shape of this game.
If the home support were nervous and edgy throughout the first-half, even with their team in front, this soon turned to dismay in the second.
Own goals from substitute Kyle Lafferty and Lee McCulloch on 49 and 59 minutes respectively put the visitors in dreamland.
And even they looked shocked when Pablo Brandan drilled a left foot free-kick from 30 yards beyond Allan McGregor to make the scoreline 4-1.
Smith elected to leave Kris Boyd and Lafferty on the bench with Old Firm hero Kenny Miller named as the lone striker.
With Madjid Bougherra out with a knee injury picked up at training last night Rangers started with Steven Whittaker, David Weir, McCulloch and Sasa Papac in front of McGregor.
In midfield Mendes, Kevin Thomson and Davis featured in the centre with Jerome Rothen and Steven Naismith supporting Miller from the right and left flanks.
The 4-5-1 formation utilized by Smith early on was not a surprise, especially with Bougherra out, and Rangers got off to the best possible start.
A corner came in from Rothen and when the ball was cleared it fell to Mendes 25 yards out.
The Portuguese ace tried his luck with a long range effort and a deflection from Ricardo Vilano sent the ball looping over keeper Daniel Tudor.
The early strike was just what was required and the Light Blues immediately went in search of a second.
On ten minutes a Mendes free-kick from the left was flicked on by Miller but his header went inches over the bar.
Papac, the hero for Rangers against St. Johnstone, then showed his attacking intent when he let fly with a 25 yard effort which went high and wide.
The Bosnian then slid a terrific low cross in to Steven Naismith but it was a foot in front of the Scottish international who had found space behind the visitor’s defence.
At the half hour mark Rangers looked in control but this all changed when Urziceni pulled themselves back in to the game.
Brandan found acres of space on the left and his low cross was drilled home by Marius Bilasco from six yards with McGregor stranded.
Rangers then had the perfect opportunity to regain their lead when referee Eric Bramhaar awarded a penalty after Bruno Fernandes handled the ball in the box.
Davis took the resulting spot kick but Tudor dived to his right to deny the Northern Ireland international.
The first-half ended level but the fans’ reaction at the whistle was one of frustration.
At the start of the second-half the injured Mendes made way for Lafferty as Rangers changed to a 4-4-2 formation.
But on 48 minutes the players in blue were given another warning when Bilasco blasted a 30 yard shot which had to be tipped over by McGregor.
From the resulting corner the ball was cleared to Iulian Apostal and his low cross was flicked in to the net, via the back post, by the unfortunate Lafferty.
Unirea’s second goal once again stunned the home support but disaster was to follow on 59 minutes.
An in-swinging cross from Tiberiu Balan caused mayhem in the box and McCulloch headed the ball past a bewildered McGregor.
Like against Sevilla Rangers looked shell shocked on the pitch and with fans already leaving the stadium with 30 minutes remaining this was already looking like a night to forget.
With heads down and defeat already looking inevitable the Romanians were to pile on more misery on 63 minutes after they were awarded a free-kick 30 yards from goal.
Brandan stepped up and his drilled effort appeared to go through the wall before beating McGregor low to his right.
Steven Naismith came close to finding the net in the last minute but his header went tamely wide of the target.
This summed up Rangers’ evening; it was one of desperate disappointment and at the final whistle the players looked mentally shattered as they headed down the tunnel.
Unirea came to Glasgow expecting to lose yet they travelled back to Romania wondering how they managed to secure a 4-1 victory.
Big questions will now be asked of this Rangers team who now have three group games to save their European ambitions for the season.