Substitute Rod Wallace laid the ball off and the German midfielder drove a terrific low shot in off the left hand post to sent Ibrox into raptures.
The lead is a slender one, but now Rangers have a realistic chance of making it through to the fourth round and it’s all thanks to Albertz.
However, it looks as though Rangers will have to try to progress without captain Barry Ferguson as he was booked in 33 minutes for a foul on Marian Hristov and has now collected three yellow cards in Europe this season.
Suitably buoyed by their Sunday roasting of Celtic, Rangers had power, pace and precision in their early play but they key issue was that they could not make their dominance pay.
The created so many chances in the first half it was almost unbearable for Dick Advocaat on the bench as each one was spurned and somehow the Germans managed to get to half-time without losing a goal.
Just like Sunday, Rangers might have scored after only two minutes and the fact that they did not was as much down to the the misfortune of Michael Mols and the fortune of Kaiserslautern keeper Georg Koch.
It was Ronald de Boer who started the move with a great spin in midfield and a super ball out to Kenny Miller who had broken free on the right, His cross was low and hard and met by Mols but his shot struck the started Kock and the chance was gone.
Rangers were given a warning, however, about the danger of Youri Djorkaeff when he struck a fierce right foot shot in six minutes which Stefan Klos blocked superbly after Andreas Buck had crossed from the right.
It was about all the Germans had to offer, however, and Rangers were in again in 15 minutes. Lorenzo Amoruso, a tower of strength against Celtic, showed great vision to release Jorg Albertz on the left but he shot against Koch when he should have scored.
Then in 26 minutes the pace of Miller destroyed the Germans and his cross was met by skipper Barry Ferguson but again Koch got a block on the shot and Rangers were frustrated once Moore.
Mols and Koch were involved in an altercation to earn bookings but it did not stop the play from flowing towards the Kaiserslautern goal. De Boer tried his luck from distance in 29 minutes but Koch was in the right place while Miller and Arthur Numan both sliced wide when they should have done better.
It was all Rangers other than sporadic movements from the Germans but the goals just would not come. Koch spilled Albertz’s freekick in 35 minutes and then thre ball seemed to strike Murat Yakin’s hand, but no penalty was given and that seemed to sum up Rangers’ night.
It was equally frustrating in the early moments of the second half. Ranges still had the upper hand but they had lost the art of creating chances which as even more alarming for Advocaat.
The Germans lapped it up, of course, and resorted to feigning injury in an attempt to upset Rangers’ rhythm. Fortunately French referee Gilles Veissiere was not fooled when Jorgen Pettersson threw himself to the floor in 56 minutes and booked him.
Rangers had to be wary the counter-attack and they were nearly caught out in 60 minutes when Buck burst forward but Amoruso made a brilliant intercepting tackle to snuff out the danger.
The Ibrox supporters willed a goal and it nearly came about in 65 minutes when Yakin brought down Mols just outside the box to earn a booking. Albertz bent the freekick around the wall but Koch was equal to it.
Then two minutes later Amoruso thundered a freekick from a tighter angle which Koch again blocked but there were no Rangers players on hand to pick up the rebound.
It was becoming more and more desperate for Rangers and Neil McCann was sent into the game in 69 minutes to try and make something happen but still the goal would not come.
Kaiserlautern were then reduced to 10 men when Jorgen Petterson was sent off for a second bookable offence.
However, finally, with two minutes remaining Albertz came up trumps with the precious strike which gives Rangers every chance now of making it through to the fourth round in the spring.
It was substitute Rod Wallace who set up the chance with a neat lay-off on the edge of the box and Albertz hammered the ball into the net off the left hand post with his right foot, would you believe.
The job is still not done but holding a one goal lead is so crucial. It was late but it was worth it .
RANGERS: Klos; Wilson, Konterman, Amoruso; Reyna, Ferguson, de Boer (McCann 69), Albertz, Numan; Mols (Wallace 85) Miller. Subs – Ricksen, Dodds, Tugay, Christiansen, Vidmar.Bookings: Mols (26) Ferguson (33)
KAISERSLAUTERN: G. Koch; Yakin, Ramzy, Komljenovic; H. Kock, Buck (Reich 90), Grammozis, Djorkaeff (Strasser 82), Hristov; Lokvenc (Klose 56), Pettersson. Subs – Weidenfeller, Schjonberg, Marschall, Adzioc.Sent off: Pettersson (80) Bookings: G. Koch (26), Yakin (65)
Ref: Gilles Veissiere (France).Att: 47,279.