Milan travelled to Glasgow in dreadful form but broke the deadlock from their first corner kick on 13 minutes, with Kaka heading home from close range.
Here, Sports Mole looks at what went wrong for Neil Lennon's men on a miserable night at Celtic Park which saw them crash out of Europe altogether.
On target: 10
On target: 4
Was the result fair?
Milan proved to be a clinical, effective counter-attacking team who carried out their gameplan to perfection. Celtic lacked the quality to match their hard-working display and were ultimately well beaten.
For large parts of the match Celtic were more than a match for their Milanese counterparts, but all their efforts to press and harry were undone by sloppy defending from set pieces. Giorgios Samaras was also starved of service in the final third, reduced to heading on scraps as the hosts were restricted to threatening from set pieces.
Massimiliano Allegri will be delighted with what his under-fire side offered up tonight, regularly finding Balotelli with penetrative passes and using Nigel de Jong and Riccardo Montolivo as a midfield forcefield never shirking their responsibilities. A job well done for a side without a win in seven matches before travelling to Glasgow.
Sports Mole's man of the match
Mario Balotelli: Milan's main man has come under fire after a string of poor performances in recent weeks, but was nothing short of sensational tonight. His strong work to hold the ball up gave Milan a platform to build on, while his well-taken third came out of almost nothing after he turned Montolivo's long ball into a sprint on goal. The Rossoneri desperately need their forward talisman to maintain this attitude in Serie A to reverse their poor domestic start.
Celtic's defence will have to take this award collectively for a truly shambolic effort defending a corner kick early on. Valter Birsa's delivery was allowed to find Kaka in the six-yard box without a single Green and White shirt near him, something Lennon will no doubt be seething about as they gave away a cheap early goal.
Cüneyt Cakir regularly annoyed Lennon by breaking up play due to persistent fouling, not allowing Celtic to build any pressure on the visitors. His performance was on the whole effective though, giving both teams the freedom to express themselves.
Celtic: Lennon's men are now reduced to focusing on the fight for domestic domination, hoping to extend their 13-match unbeaten run in Scotland against Hearts in the Scottish Cup on Sunday.
Milan: Allegri's men will hope to use their encouraging European form as a catalyst to climb the Serie A table when they meet Catania on Sunday.