The Serie A side drew a blank in their own backyard for the third time this term, following successive league defeats to Sampdoria and Atalanta
The Rossoneri went close on a few of occasions, with Mathieu Flamini, Urby Emanuelson and Stephan El Shaarawy all testing Silvio Proto in the visitors' goal.
However, for the most part, the home side struggled horribly to impose themselves on the game and were grateful to a wasteful finish from Lucas Biglia for sparing them from what would have been a third successive defeat at the Giuseppe Meazza this season.
Indeed, with Milan having lost their first two home games in Serie A, against Sampdoria and Atalanta, it was hardly surprising that Anderlecht showed no fear of their illustrious rivals. However, the level of control they exerted over the first half was nonetheless startling.
They had the lion’s share of possession and repeatedly called Christian Abbiati into action, with Guillaume Gillet going closest for the visitors with a near-post strike, after a rampaging run down the right-hand side.
The one plus side for Milan was that when they did get some time on the ball, they looked the far more likely to score. Indeed, Flamini really should have broken the deadlock 18 minutes in after latching onto a clever lay-off from Kevin-Prince Boateng, but the Frenchman’s low drive was saved by the feet of Proto.
The latter came to Anderlecht’s rescue again just after the half-hour mark when he parried away Emanuelson’s instinctive half-volley, after the Dutchman’s well-timed run in behind the visitors’ defence had been superbly spotted by Nigel de Jong.
It was Anderlecht, though, who had the best chance to break the deadlock early in the second half, but after being put through by the most delightfully-weighted through-ball from Dieudonne Mbokani, Biglia blazed over the bar.
That let-off prompted Massimiliano Allegri into action and the under-fire coach replaced the strangely subdued Boateng with El Shaarawy, who immediately injected some life into the Rossoneri attack.
Indeed, the young striker saw a near-post header saved by Proto before then playing a clever ball inside to Emanuelson, but the former Ajax man’s subsequent strike flew high and wide.
However, despite El Shaarawy's promptings, the hosts were unable to fashion a late winner, meaning they will now travel to Russia on October 3 to face Zenit in dire need of a win. Anderlecht, meanwhile, will take great confidence into their meeting with Malaga on the same night.