Peter Lovenkrands might have won the game with nine minutes remaining but he inexplicably headed wide from inside the six yard box.
Rangers are still very much alive but they will probably need at least two points from their remaining matches.
Rangers could not have wished for a better start when they roared into the lead with just two minutes on the clock.
It was all about aerial power which sent the traveling fans into raptures as the Light Blues made full use of a set piece situation.
Stevie Thompson was brought down just outside the box on the right side. Brahim Hemdani swept the free kick to the back post, Sotirios Kyrgiakos headed it back across the face of goal and Prso was there to nod the ball into the net.
Rangers should have consolidated after such an early breakthrough but they only held their lead for five minutes.
Some nightmarish defending allowed Artmedia to equalize and it turned the game back in the favour of the Slovakians.
Rangers did not deal with Branislav Fodrek’s corner from the right and the ball broke to captain Balazs Borbely who had the simplest of chances to fire home from close range.
The Slovakians then took control with some slick passing largely orchestrated by Jan Kozak in midfield and Rangers looked decidedly ragged.
Ronald Waterreus had to touch away a decent strike from Ales Urbanek which had taken a deflection off Julien Rodriguez in 12 minutes. Then in 30 minutes striker Lukas Hartig missed a glorious chance when he headed wide from Kozak’s cross.
In fairness, Thompson shot just wide in 14 minutes and Fernando Ricksen tested Juraj Cobej from 25 yards in 34 minutes but he was never going to beat the Artmedia keeper with such a straight strike.
And as the first half drew to close Rangers suddenly found their form again and began to dominate.
Peter Lovenkrands, who had been largely anonymous, shot just over the top in 35 minutes and then a minute before the break the Ibrox men roared into the lead again.
Barry Ferguson won a corner after a terrific run and it was worked short to Prso. The talismanic Croatian twisted and turned and then delivered a fantastic cross to the backpost where Thompson powered in a wonderful header.
It was a fantastic moment for the big striker who claimed his first goal in the Champions League proper.
Sadly for the Ibrox men, the goal only seemed to inspire Artmedia who might have scored twice in the early moments of the second half and then claimed an equalizer which was a disaster from Rangers’ point of view.
Rodriguez inexplicably lost the ball to Hartig inside the box and allowed him to cut back for Fodrek who should have scored but blazed over the bar.
That came in 52 minutes and three minutes later Waterrues was beaten by Obzera’s powerful drive from the edge of the box but Olivier Bernard saved Rangers by clearing off the line near the right hand post.
However, Rangers did no survive in 59 minutes when a terrible lack of communication between Hemdani and Waterreus cost them so badly.
Hemdani failed to control Alan Hutton’s throw-in, a Rodriguez clearance bounced awkwardly just outside Rangers’ penalty box and Waterreus’ clearance, under pressure from Brahim, dropped for Kozak who swept the ball into the gaping net.
It was like a sick slapstick comedy and the Slovakians could not believe their luck, Alex McLeish undoubtedly cursed his.
He sent on Franny Jeffers for Thompson with 21 minutes left and Rangers worked tirelessly to try to grab a winner.
Peter Lovenkrands should have provided it but missed an absolute sitter with just nine minutes remaining.
Bernard’s cross from the left came off the bar and broke to Alan Hutton who put the ball right on Lovenkrands’ head inside the six-yard box. Incredibly he headed wide with the goal gaping.
It might be a costly miss but Rangers are still fighting in the Champions League.
ARTMEDIA: 1-Cobej; 21-Petras, 2-Debnar, 4-Durica, 22-Urbanek; 8-Vascak (13-Tchur 83), 25-Kozak, 17-Borbely, 20-Fodrek; 12-Obzera (3-Stano 87), 16-Hartig (14-Halenar 72).
Subs not used: 18-Kamenar, 10-Mikulic, 23-Konecny, 14-Burak.
Bookings: Fodrek (87)
RANGERS: 25-Waterreus; 20-Hutton, 14-Kyrgiakos, 16-Rodriguez, 3-Bernard (24-Murray 90); 2-Ricksen, 7-Hemdani, 6-Ferguson, 26-Lovekrands; 19-Thompson (21-Jeffers 69), 9-Prso.
Subs not used: 1-Klos, 5-Andrews, 8-Rae, 17-Burke, 31-Namouchi.
Bookings: Kyrgiakos (79), Ferguson 85
Ref: Florian Meyer (Germany)
Key Man – Dado Prso