Torres scored twice for Chelsea
Holders Chelsea have been knocked out of the Champions League at the group stage despite beating Nordsjaelland, while Celtic progressed to the knock out stage.
Juventus's victory over Shakhtar Donetsk made Rafa Benitez's first win in charge of Chelsea academic, reports the BBC.
Each side missed a penalty before David Luiz scored from the spot, Fernando Torres doubling the lead before half-time as Chelsea guaranteed third place.
Joshua John replied before Torres added his second, with Gary Cahill, Juan Mata and Oscar also scoring after the break.
At Old Trafford, Manchester United suffered their first home defeat in the Champions League for three years on a night of obvious frustration for Sir Alex Ferguson.
It is the first time United have failed to score at Old Trafford since being held by Rangers back in September 2010.
Luis Alberto's goal early in the second half proved the difference, with the Spaniard beating United goalkeeper David de Gea with a 25-yard strike.
United had already qualified for the last-16 as winners of Group H.
And in Glasgow, Kris Commons' late penalty against Spartak Moscow ensured that Celtic progressed nervously into the last 16 of the Champions League.
Celtic went ahead after Gary Hooper pounced on a mistake from Juan Insaurralde to fire in from 18 yards.
But Brazilian striker Ari levelled with a chip over goalkeeper Fraser Forster that Kelvin Wilson could only divert into his own net.
However, Commons scored from the spot after a foul on Georgios Samaras.
It was a somewhat harsh decision on Spartak defender Marek Suchy, but it gave the winger the chance to score the goal that ensured that Celtic progress as Group G runners-up behind Barcelona.
Celtic had to better Benfica's result in the Nou Camp, but an under-strength Barca could do no better than a goalless draw in Spain.
That was enough for Celtic to make the last 16 for the third time in the Scottish champions' history after a game that both sides finished with 10 men after Commons was stretchered off after a foul that led to Kim Källström being shown a red card.
In other games Barcelona was held to a goalless draw at home to Benfica, Bayern Munich beat BATE Borisov 4 – 1, Galatasaray qualified second behind Manchester United after beating Braga 2-1 and Lille lost 0 – 1 to Valencia.
Celtic 2 - 1 Spartak Moscow
Chelsea 6 - 1 Nordsjaelland
Man Utd 0 - 1 CFR Cluj-Napoca
Barcelona 0 - 0 Benfica
Bayern Munich 4 - 1 BATE Borisov
Braga 1 - 2 Galatasaray
Lille 0 - 1 Valencia