Celtic have reached the Europa League latter stages after scraping through from their Uefa Champions League group on goal difference.
Craig Gordon was the first to be called into action, saving excellently from Kums after a Onyekuru corner.
The duo linked up seconds later with the Nigerian forward seeing his shot go high and wide.
Hein Vanhaezebrouck’s side were in control early on and with only 8 minutes gone, Obradovic shot over as the Hoops failed to get into their rhythm in the opening stages.
James Forrest was fouled on the right and that encouraged the big men from the back to join the attack. Jozo Simunovic had an effort at goal but it was blocked as Brendan Rodgers’ side tried to get a foothold in the tie.
Adrien Trebel saw two efforts saved by Gordon as the Belgians remained in command at Parkhead.
Dendoncker had the final effort of the first-half which went wide. It was a poor 45 minutes for the Scottish champions. The only positive they can take is that they were still on level terms at the interval – meaning Anderlecht still required 3 goals to oust Celtic from third place in Group B.
Rodgers wanted a reaction from his lacklustre side and made two changes at the break. Tom Rogic and Oliver Ntcham came on for Scott Sinclair and Stuart Armstrong as Celtic changed formation.
The Celts certainly did that as Ntcham fired wide before Dembele, Forrest and Simunovic saw their efforts kept out by goalkeeper Boeckx.
Pieter Gerkens headed wide but another header just moments later would open the scoring.
As the ball was floated in from the right, Simunovic got the unfortunate touch as he tried to clear the danger, which went past Gordon and in off the post.
With just under 30 minutes remaining, Celtic knew how important it was not to concede again to give the Belgian club any more confidence and momentum.
This pushed the hosts further forward with the Croatian defender almost making amends immediately, as he had a header saved on 67 minutes.
Frenchman Ntcham then had another effort blocked before his compatriot Dembele shot wide after being set-up by Tierney.
Josue replaced Kara in Vanhaezebrouck’s first switch of the evening while Rodgers made his final change of the game with another Frenchman, Odsonne Edouard – on loan from group rivals PSG – replacing Dembele with 16 minutes left.
The game was swinging from end to end: Mikael Lustig had an effort saved at one end before Sofiane Hanni also failed to score with Gordon being up to the task once more.
Trebel was next to have a dig but he was off target before the Belgian Pro League side made another tactical substitution with Gerkens going off, to be replaced by Teodorczyk.
Despite the effort and determination of both sides, the game began to fizzle out. Ntcham had a third effort but was foiled once more by Broeckx.
Appiah was brought off for Bruno as injury time approached but there was no late drama in Glasgow this evening as the two further goals required to see Anderlecht leapfrog Celtic and progress into the Europa League never came.
It was a disappointing evening for Rodgers’ men but the main thing for the Scottish side is that they will be in Europe post-Christmas.
FULL-TIME: Celtic 0-1 Anderlecht