Bonaventure Kalou was the striker who broke Rangers hearts with two well taken goals.
With AK Graz winning their match in Austria it meant the Gers had to take something out of this match but there was no doubt the French side deserved their victory.
Rangers were stunned when they lost a goal after only nine minutes. Benjani Mwaruwari played a good ball into the box and after hitting the bar with his first effort, Kalou tapped in the rebound.
The pace and power of the French side was troubling the home team but Benoit Cheyrou's long-range effort lacked the power to trouble Stefan Klos in the Rangers goal.
From Gregory Vignal's free-kick Hamed Namouchi headed into the side-netting at the back post with many in the ground thinking he had scored.
Nacho Novo then slid a superb pass through to Dado Prso but neither Namouchi or Shota Arveladze could reach his cross.
Auxerre nearly went two up when Cheyrou's pass put Mwaruwari clear but the striker mis-timed his shot.
Rangers came close to equalising when Novo's pass found Prso in the box. The Croatian striker burst between two defenders but his left-foot shot was just off target.
In a swift counter-attack just before half time Bob Malcom's pass found Fernando Ricksen but his cross to the back post was headed over by Prso.
Rangers let in another goal at the start of the second half when a poor header by Zurab Khizanishvili allowed Mwaruwari to find Kalou who skipped past Jean-Alain Boumsong before sliding the ball past Klos.
It left Rangers with a mountain to climb and in truth the Ibrox side never looked like reducing the deficit hard though they tried.
Prso's pass released Novo whose shot was pushed out by Fabien Cool but Arveladze could not reach the loose ball. Namouchi's cross was then well held by the French keeper.
Alan Hutton, who had come on for the ineffective Khizanishvili, sent in a superb cross but Prso's header was held under his crossbar by Cool.
Arveladze just failed to reach Namouchi's cross before Vignal tested the keeper with a long-range effort but in the end Auxerre held out comfortably.