FC Copenhagen 1-2 Rangers (Rangers win 3-2 on aggregate)
Mikel Arteta put Rangers ahead in Denmark from the spot
Shota Arveladze scored a crucial late winner as Rangers qualified for the Champions League group stage for the first time in three years.
Rangers travelled to Denmark as underdogs following a 1-1 draw in the first leg at Ibrox.
It looked like a second-half Mikel Arteta penalty would be enough to give the debt-struck Scottish champions the £10m boost expected to come from qualification.
But Copenhagen substitute Alvaro Dos Santos pounced on some indecision in the Rangers defence to equalise seven minutes from the end, only for Arveladze to pounce three minutes later.
Rangers had suffered a blow before kick off, when their most experienced defender, Craig Moore, lost his battle to recover from a hamstring injury.
Christian Nerlinger was a surprise starter in midfield alongside Barry Ferguson, the club captain who appears likely to get his wish to be transferred to the English Premiership.
Everton manager David Moyes was in the crowd to monitor the player he wants to sign.
The match was a bad-tempered affair and Peter Nielsen went in with his studs high on Michael Ball's thigh but escaped a booking as the Rangers defender received early treatment on the sidelines.
A poor clearance from Ricksen handed Ole Norregaard an opportunity for a shot from 22 yards, but the midfielder's low drive swept wide of the post as well as Klos.
Nielson scraped the crossbar with a curling free kick conceded by Khizanishvili following another loose pass by Ricksen.
Rangers' first threat came after 22 minutes, with Ferguson pulling the strings in midfield, but De Boer's 20-yard drive curled well wide after a neat touch into his path from Michael Mols.
Rangers made the breakthrough seven minutes after the break.
Goalkeeper Raboczki spilled a drive from Ball following a free kick and Rooba pulled down Mols as the Dutchman tried to pounce on the rebound.
Arteta stepped up to blast the penalty kick high into the net.
Shota Arveladze poked home Rangers' winning goal
It was nearly two but Raboczki just diverted De Boer's dangerous cross with Arveladze waiting to pounce.
Copenhagen pressed forward and Rangers' Henning Berg was injured as he helped ease the pressure.
Berg was replaced with Bob Malcolm, but Rangers were still dangerous and tidy play by De Boer set up Arveladze for an overhead kick that flew a couple of yards wide.
Rooba rose above his new marker to head wide from eight yards and Rangers failed to heed that threat when substitute Santos pounced to force the ball past Klos.
But Rangers were not to be denied and after Nerlinger headed the ball into the box, Arveladze reacted quickly with an acrobatic volley that could prove vital to his club's finances.
FC Copenhagen: Raboczki, Albrechtsen, Svensson, Tobiasen, Rooba, Norregaard, Nielsen, Mykland, Roll Larsen, Jonsson, Zuma.
Subs: Kihlstedt, Pettersson, Zivkovic, Christiansen, Svard, Moller, Dos Santos.
Rangers: Klos, Ricksen, Berg, Khizanishvili, Ball, Arteta, Ferguson, Nerlinger, Arveladze, de Boer, Mols.
Subs: Malcolm, Vanoli, Thompson, Capucho, Ross, McGregor, Hughes.
Referee: Zeljko Siric (Croatia)