Under pressure manager Alex McLeish made three changes from Saturday with Kyrgiakos, Rodriguez and Thompson replacing Malcolm, Andrews and Burke.
Beleaguered Rangers got off to the perfect start, taking the lead in three minutes when a Hemdani free kick found Kyrgiakos at the back post, his header across the face of goal being headed into he net from point blank ranger by Dado Prso.
The huge travelling support could never have dreamt of a such a superb start, but they were soon brought back down to earth five minutes later when Artmedia levelled matters, Balarzs Borbely finding himself free and in space following a Branislav Fodrek corner, turning the ball home with Ricksen slow to close him down.
Rangers, undaunted, continued to take the ball to their opponents at every opportunity - Thompson’s turn and shot from a Hemdani pass whistling just past in 14 minutes.
Five minutes later Jan Kozak tested Ronald Waterreus with a 25 yard shot that the keeper held, and the Dutchman was again equal to the task in 32 minutes in dealing with a 20 yard shot from Blazej Vascak.
Rangers were giving as good as they got however, sixty seconds alter Ricksen's 22 yard volley from a Prso knockdown was held by Juraj Cobej.
The Scottish champions regained the lead on the stroke of half time when THompson headed home a Prso cross.
There was yet more drama to unfold before the interval however - Kozak's in-swinging 40 yard free kick being fumbled by Waterreus then Peter Petras’s 25 yard shot flashing over. But Rangers survived to reach the dressing room ahead.
The Slovakians restarted on the offensive. Fodrek shooting over an open goal in 52 minutes after Lukas Hartig had forced an opening down the left. Two minutes Olivier Bernard cleared off the line from a 20 yard Branislav Obzera shot.
The scores were levelled in 58 minutes - and if the first goal had been down to defensive sloppiness the second was a misunderstanding between keeper and defence allowing Kozak to rifle his shot into and unguarded net.
Both sides continued to attack in search of an elusive winner, Ranges coming agonisingly close in 80 minutes when a Bernard cross cum shot came off the face of the crossbar - Ricksen seizing on eh loose ball to chip across of the goal where Lovenkrands managed to head wide of an empty net.
A sporting game almost boiled over in the closing seconds when Rangers substitutive Franny Jeffers went in on Cobej in pursuit of a Lovenkrands header but peace was quickly restored and the final whistle left Rangers in second place in the group on five points, with Inter Milan having defeated Porto 2-1 in tonight’s other group game.
Artmedia Bratislava : Cobej, Petras, Debnar, Durica, Urbanek, Vascak (Tchur 83), Kozak, Borbely, Fodrek, Obzera (Stan 87), Hartig (Halenar 73). Subs Not Used : Kamenar, Mikulic, Konecny, Burak.
Goals : Borbely 8, Kozak 59. Booked : Fodrek.
Rangers : Waterreus, Hutton, Kyrgiakos, Rodriguez, Bernard (Murray 90), Ricksen, Ferguson, Hemdani, Lovenkrands, Thompson (Jeffers 70), Prso. Subs Not Used : Klos, Andrews, Alex Rae, Burke, Namouchi.
Goals : Prso 3, Thompson 44. Booked : Kyrgiakos, Ferguson.
Att : 6,527
Ref: Florian Meyer (Germany)