Walter Smith’s side attempted in vain to find the vital goal they needed but could not break down a stubborn backline that was marshalled confidently by the experienced Cesar Cruchaga.
In the end it was Pierre Webo’s 71st minute winner that put the home side through although they already had their noses in front with an away goal and Osasuna’s name will now go in the hat for Friday’s quarter final draw in Glasgow
The Gers’ gaffer decided to only make one enforced change to his starting eleven with Gavin Rae replacing Barry Ferguson and also being given the captain’s armband for the night.
The 29-year-old was asked to play in the hole in front of the Osasuna backline and support lone striker Filip Sebo.
The atmosphere in the stadium was electric prior to kick-off but Rangers were almost caught on the back foot in the first minute.
Ugo Ehiogu, the hero against Celtic with his fantastic overhead kick, played a slack pass infield and when the ball was fed to Romeo his skewed effort failed to trouble to McGregor.
Osasuna again made their intentions clear two minutes later when playmaker Juanlu, who was excellent on the night, launched a left-foot free-kick from 25-yards which was inches over the bar.
The early scares sparked the Blues into life and Charlie Adam had a similar opportunity but chose to drive a low effort into the box before the ball was cleared to safety.
Alan Hutton has been in excellent form in recent matches but the young right-back put his name in the referee’s notebook for a second poor challenge after only 11 minutes which would have ruled him out of the club’s next European match had the club progressed further.
Despite being under substantial pressure in the first 20 minutes the game remained goalless although Smith must have been disappointed with his player’s inability to hold on to the ball and create any good chances.
At this stage Osasuna were without doubt the dominant side and they should have taken the lead prior to the half-hour mark.
Romeo, who was selected ahead of Raul Garcia, played a clever free-kick from the left wing to Juanlu but the Osasuna no. 20 slipped before scooping the ball over the bar from 10 yards.
With the first-half coming to an end Rangers gradually started to get themselves into the match and could have had their noses in front with the last opportunity.
Kevin Thomson flighted a delightful free-kick to Charlie Adam who was unmarked at the back-post.
But to the frustration of his teammates he headed the ball into the stands when several players were shouting for it to be put into the six yard box.
The Light Blues ended the half confidently and, had they started the match in this fashion, the scoreline might not have been sitting goalless.
Nevertheless, Smith would have been buoyed with his side’s improved performance in the closing stages and would have been hoping for more of the same after the restart.
Neither manager made any adjustments to their team as the referee got the second-half underway and the Gers were perhaps a bit lucky not to give away a penalty when the ball looked to strike the arm of Ian Murray inside the 18-yard box.
Referee Claus Bo Larsen from Denmark waved away the home side’s appeal much to the frustration of the vocal club’s vocal supporters.
On 50 minutes Rangers could, and should, have taken the lead when Gavin Rae latched on to the ball after a defensive error.
The stand-in skipper moved into the 18-yard box and had time to look up but his tame effort was blocked by Cruchaga.
With his side needing a goal to have any chance of progressing Smith was quick to make his first change with Chris Burke replacing Kevin Thomson on 51 minutes.
And with time ticking away the tension inside the Reyno de Navarra Stadium was starting to rise with Osasuna determined to hold on to the slender advantage that would take them through.
It was not long before the Gers’ management team made their second switch with Dado Prso going on for Filip Sebo who had again worked hard for his team and the Croatian tried to use his vast experience to keep the ball in Osasuna’s half of the pitch.
With Rangers pushing forward it was inevitable that gaps would be left in the Gers defence and they were to be punished on 71 minutes.
Substitute David Lopez found space on the right and when his low cross was missed by David Weir, Webo was on hand to drive a low shot pass McGregor at his near post.
The goal was to come against the run of play as Rangers were in the ascendancy and it left Smith with no option but to have one last throw of the dice by giving Kris Boyd a run-out.
The hitman was to replace Rae on 72 minutes and immediately joined Dado in attack.
This last ditch attempt to get a goal almost paid dividends when Ehiogu moved up the pitch for a free-kick and was unlucky not to find the net but, in the end, it was to be a frustrating evening for the Gers.
The players could not be falted for their effort but they found themselves up against a team that were well organised and few could argue that the Spaniards deserved to go through on the back of their displays in both legs.
Smith’s side, however, have no time to dwell on this defeat as they must now rise again and be fully focused for Saturday’s hugely important clash against Aberdeen at Ibrox.