GettyImagesTeenager Tom Watt coolly fires home Celtic's second against Barcelona
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It was a Group G clash that the Hoops were not supposed to win but the east end of Glasgow exploded in the 21st minute when midfielder Wanyama headed in from a Charlie Mulgrew corner.
It was backs-to-the-wall stuff for most of the game for the home side as the star-studded visitors hit the woodwork twice and goalkeeper Fraser Forster pulled off a number of vital saves.
But in the 83rd minute 18-year-old Watt, on for Mikael Lustig to make his debut in the competition, raced away to score the second, leaving Lionel Messi's late strike a consolation.
Celtic, with seven points from four games, two less than leaders Barca, travel to Benfica before hosting Spartak Moscow in their final group fixture and will surely fancy their chances of reaching the knockout stages of the competition.
The crossbar denied Oscar Cardozo a hat-trick but he did enough to keep Benfica alive in Group G with a 2-0 victory over 10-man Spartak Moscow.
Cardozo scored twice in the second half and then saw his penalty rattle the bar after Nicolas Pareja had been sent off for bringing him down in the area.
But while there was no matchball for Cardozo, there were three vital points for Benfica to move them off the bottom of the group, even if their chances of sneaking into the knockout stages were hugely complicated by Celtic's shock defeat of Barcelona.
Victor Moses came off the bench to score an incredible last-gasp winner as Chelsea survived a Shakhtar Donetsk onslaught to keep their Champions League fate in their own hands with a 3-2 victory.
GettyImagesVictor Moses heads home in the 94th minute to make it Chelsea 3-2 Shakhtar
The Blues were in danger of being the first holders to crash out of the competition before Christmas as former target Willian twice cancelled out almighty howlers from goalkeeper Andriy Pyatov, which gifted goals to Fernando Torres and Oscar, the latter's fourth in as many Champions League games.
But late substitute Moses nodded home Mata's 94th minute corner to steal a barely-believable victory that put Chelsea level on points with their opponents at the top of Group E with two games remaining.
Juventus registered their first Champions League win of the season after a comfortable 4-0 victory over FC Nordsjaelland.
First-half strikes from Claudio Marchisio, Arturo Vidal and Sebastian Giovinco, plus a second-half header from Fabio Quagliarella were enough to see off the Norwegian champions as the Italians finally tasted victory after three successive draws.
Late goals from Robin van Persie, Wayne Rooney and Javier Hernandez saw Manchester United come from behind to secure a 3-1 victory in Braga and with it their place in the last 16 of the Champions League.
A United side showing six changes from Saturday's Premier League win over Arsenal struggled to get going in the first half and the hosts went in front shortly after the interval through a penalty from Alan.
GettyImagesRobin van Persie celebrates the first of Man United's trio of goals as they came from behind to win at Braga
However, as they have done so often this term after conceding the first goal, the Red Devils fought back to win thanks to substitute Van Persie's 80th-minute effort from outside the box, a Rooney spot-kick five minutes later and Hernandez's stoppage-time strike. It leaves Group H leaders United on 12 points and guaranteed to go through as group winners.
Burak Yilmaz grabbed a hat-trick as Galatasaray kept their hopes of reaching the knockout stages alive with a fine 3-1 win at CFR Cluj in Group H.
The Turkish side went into the game without a win in the competition so far and knowing only a win would realistically be enough to give them hope of going through behind group winners Manchester United.
Bayern Munich surged to the top of Champions League Group F with a 6-0 hammering of pointless Lille.
Claudio Pizarro completed his hat-trick in the 33rd minute, by which point Bayern led 5-0 with Bastian Scweinsteiger and Arjen Robben both striking from free-kicks.
Salomon Kalou pulled one back from long range but substitute Toni Kroos was quick to add his name to the list of scorers as Bayern moved to nine points ahead of their second meeting with fellow pace-setters Valencia.
Valencia completed a double over BATE Borisov with a 4-2 victory that keeps them level on points with Bayern at the top of Group F.
Goals from Jonas Oliveira and Roberto Soldado in four first-half minutes, the latter from the penalty spot, put the Spanish side on top at the Mestalla.
Sofiane Feghouli's second-half brace sealed victory as BATE threatened a comeback through star man Renan Bressan and Dmitri Mozolevski.
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