Juventus created few opportunities apart from an early close-range effort from striker Zlatan Ibrahimovic.
Another expensive summer acquisition Zlatan Ibrahimovic also scores twice as PSG defeats Lille 2-1.
Sweden international Zlatan Ibrahimovic doubled the advantage before halftime with his league leading 20th of the season.
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PSG's challenge will be headed by Swedish striker Zlatan Ibrahimovic, who will be returning to his former club.
New Barcelona striker Zlatan Ibrahimovic scored a dramatic late winner for the Swedes.
Thierry Henry, Ronaldinho, Carlos Tevez, Zlatan Ibrahimovic, Frank Lampard and Samuel Eto'o make up the rest of the top 10.
Zlatan Ibrahimovic sets a new record as the first player to score for six different clubs in the Champions League.
Ezequiel Lavezzi wasted the most clear-cut opportunity, racing onto Zlatan Ibrahimovic's through ball only to fire straight at the onrushing Victor Valdes.
Earlier, Barcelona surrendered vital points and had striker Zlatan Ibrahimovic shown a red card and coach Pep Guardiola sent to the stands.
Swedish football star Zlatan Ibrahimovic - whose parents came from former Yugoslavia - is a hero for many immigrant boys in Rosengard.
Inter acquired Eto'o from Barcelona in a deal finalised last month which also involved Sweden striker Zlatan Ibrahimovic and Brazil's Maxwell joining Barcelona.
The team now leads the French league, thanks mainly to the performance of Swedish striker Zlatan Ibrahimovic, who arrived in Paris in August.
Sweden got off to a dream start when Zlatan Ibrahimovic provided a cross from the right for Allback to head home from close range.
Goalkeeper Heurelho Gomes saved from Zlatan Ibrahimovic and Pato, while William Gallas kept Milan at bay with a priceless goal-line clearance from Robinho's deflected shot.
Over the course of his long European soccer career, Zlatan Ibrahimovic has been accused of many things: being too moody, playing selfishly, looking like a pirate.
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Barca also made public its annoyance at the failure of the officials to rule out Zlatan Ibrahimovic's strike, which came with the forward in an offside position.
City have reportedly made a 35m Euro bid for Barcelona striker Zlatan Ibrahimovic , although the offer doesn't appear to be high enough to land the Swede.
Alessandro del Piero is also expected to stay, while coach Didier Deschamps says that Gianluigi Buffon, Zlatan Ibrahimovic and David Trezeguet will all remain at the Stadio Delli Alpi.
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Barca will again be without injured striker Zlatan Ibrahimovic, but the Sweden international is expected to return to training before Saturday's local derby at Espanyol, the club's Web site reported.
The Italian league leaders also had their moments in front of goal but squandered chances to take the lead, with Robinho and Zlatan Ibrahimovic both failing to find the net.
In the summer the Rossoneri had slashed their wage bill by 35%, letting go a number of veterans and selling their best attacker (Zlatan Ibrahimovic) and their best defender (Thiago Silva).
Zlatan Ibrahimovic hit the set-piece against the wall before his miscued volley fell to Mellberg, whose shot was parried by Joe Hart only to bounce off Glen Johnson and over the line.
Milan (Zlatan Ibrahimovic) and Arsenal (Robin Van Persie) both have strong, tall strikers, but both are also extremely skillful, complete players who roam the attacking front and often create chances for teammates.
But the move fell through and PSG moved on to other targets, landing striker Zlatan Ibrahimovic and AC Milan teammate Thiago Silva as well as Napoli winger Ezequiel Lavezzi and Brazilian prodigy Lucas.
Last summer Milan owner Silvio Berlusconi decided that the team could no longer operate beyond its means and sold off the crown jewels in the shape of Thiago Silva and Zlatan Ibrahimovic to PSG.
Swedish striker Zlatan Ibrahimovic scored a brace to take his tally of league goals to 24 this season and give the league leaders a five-point lead ahead of second-placed Lyon's match against Marseille on Sunday.
He lost his place in the Milan starting XI when Zlatan Ibrahimovic and Robinho joined last summer, and with Antonio Cassano having signed from Sampdoria this week, there is no space for him in Allegri's line-up.
Following last year's comprehensive 3-1 aggregate defeat against Lionel Messi and colleagues in the Champions League quarterfinals, Milan overhauled their squad -- with Gennaro Gattuso, Clarence Seedorf, Alessandro Nesta and Zlatan Ibrahimovic among those moved on.
But the European champions showed no ill effects at the Nou Camp as star forwards Zlatan Ibrahimovic and Lionel Messi put on a masterclass, and unsung midfielder Seydou Keita was also to the fore with a hat-trick.
Aleksandr Ryazantsev's stunning long-range strike jolted Barca, who equalised through Zlatan Ibrahimovic's powerful finish, only for Gokdeniz Karadeniz to fire the winner following a breakaway as Pep Guardiola's side slumped to their first defeat of the season.
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