Keeper Lukasz Fabianski picked up what was deemed a Sol Campbell backpass and Falcao scored from a quick free-kick.
United have reportedly been linked with moves for Borussia Dortmund's Polish striker Robert Lewandowski and Atletico Madrid's prolific forward Radamel Falcao.
Atletico Madrid takes the UEFA Super Cup against Chelsea 4-1 and Falcao is the star of the show with a hat-trick.
Messi, who scored a world record 91 goals in 2012, is now 10 clear of Atletico's Radamel Falcao in the La Liga scoring charts.
Real also conceded first in the match against their city rivals at the Vicente Calderon -- Radamel Falcao opening the scoring in the fourth minute.
But after Rosicky was denied a penalty, Falcao poked in a Ruben Micael free-kick after Fabianski had picked up a backpass from Campbell inside the box.
Mame Diouf gave Hanover some late hope with an equalizer on 81 minutes but Radamel Falcao scored the clinching goal for Atletico in the closing moments.
"Thanks to lots of training and hard work, I was able to succeed and be able to shine above other players of my age, " Falcao said.
Porto had their best chance after 54 minutes when Hulk set up Falcao, but his finish was straight at Almunia, who held on at the second attempt.
Colombian striker Radamel Falcao scored twice to overtake Lionel Messi at the top of La Liga's scoring charts, with Atletico's thirteen points now just two fewer than Barcelona.
Radamel Falcao beat two Real Madrid players before setting up Costa, although Falcao -- one of the most coveted strikers in the world -- otherwise had a quiet evening.
Visiting Valencia took the lead in the first half through Jonas, but Atletico's top scorer Radamel Falcao immediately replied with his 22nd in La Liga this season from Arda Turan's cross.
Elsewhere, Atletico Madrid maintained their seven point lead over their city rivals in second with a comfortable 2-0 win over Levante , though their star striker Falcao limped off with injury.
After Ronaldo opened the scoring in the 14th minute with a typically impressive header, Diego Costa leveled on a counter attack in the 35th after superb work by striking partner Radamel Falcao.
After an indirect free-kick was awarded, Hansson let the hosts take it quickly and Ruben Micael rolled the ball across for Falcao to side-foot home while Arsenal were still attempting to reorganise.
Meanwhile, Radamel Falcao scored twice as third place Atletico Madrid cruised to a 5-0 win over Granada, while Real Sociedad's Imanol Agirretxe kept his side's push for Champions League football on track.
It was another moment of madness for Arsenal's stand-in number one and worse was to come as the quick-thinking Micael passed the free-kick to Falcao, who calmly slotted the ball into the net.
Porto president Pinto Da Costa has made it clear that if any English clubs are interested in either of the Portuguese club's strikers, Hulk or Falcao, they will have to meet his demands.
And it was Campbell, making his first Champions League appearance since the 2006 final against Barcelona, who recovered brilliantly to tackle Falcao after the Colombian striker had cruised past the 35-year-old into the box.
Gabi dispossessed Gerard Pique and fed the ball to striker Radamel Falcao, who netted his 28th goal this season to stay third in the "Pichichi" scoring stakes behind Messi (46) and Cristiano Ronaldo (34).
Porto applied brief pressure after the interval, with Manuel Almunia saving from Falcao, but Arsenal completed the formalities and cruised into the quarter-finals with two superb goals inside three minutes just after the hour.
Falcao's fee is already the fourth-highest ever paid.
WSJ: Strikers Likely to Be Focus of Soccer's Summer Transfer Market
Falcao who has scored five goals in six qualifying games, wants the latest generation of Colombian talent to write their own records and emerge from the shadow of former great players such as Carlos Valderrama and Faustino Asprilla.
Atletico striker Radamel Falcao scored his 19th league goal this season, putting him third in the Pichichi standings behind Real's Cristiano Ronaldo -- who took his tally to 24 with a hat-trick in Saturday's 4-1 win over Sevilla.
"But clubs like City, Manchester United and Chelsea will also always try and sign the exceptional player, " added Vieira, when asked if the English Premier League champions were no longer interested in signing players such as Atletico Madrid striker Falcao, who is expected to leave the Spanish club next summer.
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