Neil Lennon's side produced one of the best results in the club's history as they claimed a 2-1 win at Parkhead.
Victor Wanyama's towering header set them on their way in the first-half, before a breakaway goal from substitute Tony Watt doubled their lead with eight-minutes left.
Lionel Messi's goal set up a frantic finale, but the Scottish champions held on to record a famous win.
Elsewhere in Group G, Benfica claimed their first win with a 2-0 success over Spartak Moscow, with Oscar Cardozo scoring twice in the second-half at the Estadio da Luz.
European champions Chelsea made hard work of their 3-2 win over Ukrainian giants Shakhtar.
Chelsea were twice ahead, only to be pegged back by the outstanding Willian. Fernando Torres got lucky after six-minutes when a failed clearance rebounded in off him, whilst Oscar scored just before the break - but each time they were pegged back by the Brazilian forward.
Then, with the game heading for a draw, Victor Moses headed home his second goal in two games to give Chelsea a hugely valuable win which takes them top of Group E.
Juventus are just behind Chelsea, after they easily dispatched Danes Nordsjaelland with a 4-0 win in Turin.
First-half goals from Claudio Marchisio, Arturo Vidal and Sebastian Giovinco set up the win before Fabio Quagliarella wrapped up the result 15-minutes from time.
Manchester United had to come from behind in Portugal before wrapping up a 3-1 win over Braga and booking their place in the knockout stages.
An Alan penalty just after the break had given Braga the lead, and then a power cut at the Municipal stadium caused a 12-minute delay, with United reacting best after re-start.
Robin van Persie levelled with 10-minutes left and then Wayne Rooney slotted home from the penalty spot to give them the lead before Javier Hernandez fired home the third in stoppage time.
United are now already through in Group H, with the second spot still open to the other three teams after Galatasaray claimed a 3-1 win in Romania over Cluj.
Burak Yýlmaz was the hero for Gala with a hat-tick, with Cluj briefly on level terms when Modou Sougou scored just after the break.
Bayern Munich went top of Group F as they knocked out French side Lille with a comprehensive 6-1 thrashing at the Allianz Arena.
Bayern were five-goals to the good by the break thanks to a Claudio Pizarro hat-trick and goals from Arjen Robben and Bastian Schweinsteiger.
Salomon Kalou pulled one back just after the break but Bayern completed the scoring through Toni Kroos.
Valencia remain level on points with Bayern after they claimed a 4-2 win over BATE Borisov at La Mestalla.
Jonas and Roberto Soldado made it 2-0 by the half-hour stage and Sofiane Feghouli added to that just after the break.
BATE then showed spirit with Bressan and Dmitri Mozolevski pulling goals back, but a second from Feghouli sealed the win.