AZ Alkmaar booked their place in the knockout stages of the UEFA Cup but left Rangers with work to do to reach the last 32.
A goal after only seven minutes from Denny Landzaat was enough to secure victory in the Dutch market town.
Rangers now go into their final group match against Auxerre needing to take something if they are to progress.
A late effort from substitute Stephen Hughes was cleared off the line otherwise Rangers would have taken a point in Alkmaar.
Dado Prso threatened first with a low 20-yard shot which goalkeeper Henk Timmer dealt with comfortably.
But AZ heeded the warning and took the lead within a minute with a carefully-crafted goal. Stijn Huysegems cut Rangers open on the left and his low cross was touched into the path of Landzaat by Martijn Meerdink and the midfielder slammed the ball past a helpless Stefan Klos.
Meerdink came close again a couple of minutes later with a controlled volley which bounced just a yard past the post.
AZ looked dangerous every time they went forward and it took a terrific save from the alert Klos to prevent Landzaat from scoring a second.
The Dutch played some fluent football at times and the pace of Huysegems was a constant source of worry for Alex McLeish's side.
Rangers tried to come back and Marvin Andrews hooked a shot over the crossbar before Peter Lovenkrands was also too high with an effort from outside the area.
Nacho Novo squandered the best chance nine minutes from the interval after some slack defending by the Dutch but he directed his effort at the goalkeeper and AZ kept their advantage.
Rangers looked ragged at times at the back and it took another fine save from Klos two minutes from the break to keep them out after Barry van Galen stole in behind the defence.
Rangers looked more purposeful at the start of the second half and Prso was not far away with a long-range effort after taking on the home defence single-handedly.
Novo then forced another save from Timmer with an angled shot which threatened to creep in at the goalkeeper's near post.
But a dreadful mistake by Michael Ball almost cost Rangers in the 65th minute when he failed to clear his lines and van Galen's header was clutched underneath the crossbar by Klos.
Jean-Alain Boumsong warmed Timmer's hands with a 25-yard shot as Rangers threatened again but the Scottish side suffered from poor delivery at set-pieces.
It was Alkmaar who dictated the pace of the game and always looked more purposeful when they attacked.
Hughes had a late chance when Andrews headed on a Fernando Ricksen corner but his effort was cleared off the line.