City were also reduced to 10 men when Kolo Toure was sent off in injury time.
Pires finished off from close range after good work from defender Kolo Toure three minutes before half-time.
The Gunners almost took the lead moments later but Given was equal to Kolo Toure's close-range angled shot.
"Perhaps we can make the quarter-finals, and then semi-finals - this is something we can achieve, " added Kolo's younger brother.
Kolo Tore almost won the points with a fizzing shot from 30 yards, which beat Green but curled agonisingly wide.
But Kolo Toure fouled Ryan Babel and Gerrard held his nerve from the spot, before Babel broke to add a fourth.
And defender Kolo Toure admitted the players need to raise their game.
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Aside from Lescott and Sylvinho, City have also recruited Kolo Toure, Gareth Barry, Carlos Tevez, Roque Santa Cruz and Emmanuel Adebayor this summer.
Chelsea goalkeeper Petr Cech had a typically solid game, his best save coming from Kolo Toure, pushing the central defender's shot past the post.
City will also be without defender Kolo Toure during January as he will be representing Ivory Coast at the African Nations Cup in Angola.
Fabiano's darting run enabled him to get to Alves' free-kick ahead of Kolo Toure and the Brazilian striker's glancing header eluded Almunia's desperate dive.
Today, Nijemo Kolo is mostly danced by village performing groups at local shows, carnivals and churches on saint days or at regional and international festivals.
Alex and Nicolas Anelka scored in the first half at the Emirates with a Kolo Toure own-goal and Florent Malouda's late strike sealing three points.
Losing the excellent Bacary Sagna to injury was a blow, but did Wenger make the right decision in moving Kolo Toure from centre-back to right-back?
But five minutes later, the Pharaohs were fortunate not to go behind when Kolo Toure's effort missed the target by a whisker, following a corner.
Arsenal added two more in the closing stages of the first-half, as Fredrik Ljungberg curled the ball past Shaka Hislop and then Kolo Toure struck.
There had been speculation surrounding Dunne's future at City following the arrival of defenders Joleon Lescott from Everton and Kolo Toure from Arsenal in big-money deals.
City had gone behind when a mix-up between keeper Joe Hart and Kolo Toure allowed Nikola Kalinic to steer in a shot from outside the area.
Arsenal pulled a goal back with 18 minutes left, Gallas turning home from almost on the line after Kolo Toure touched on substitute Tomas Rosicky's corner.
Lescott, who is the second most expensive English defender after Rio Ferdinand, is expected to form a central defensive partnership with fellow new signing Kolo Toure.
He is eager to start work and plans to head to Europe to watch the likes of Didier Drogba, Emmanuel Eboue, Salomon Kalou, Kolo and Yaya Toure.
Nijemo Kolo is a Dalmatian closed circle dance performed by communities in southern Croatia exclusively without music, although vocal or instrumental performances may precede or follow it.
Arsenal's best chance of the first half came just before the break when Robin van Persie diverted a Kolo Toure cross straight at Blues keeper Maik Taylor.
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In 2009, out went central defender Kolo Toure (another captain: Do we see a pattern here?) and center forward Emmanuel Adebayor, the second-leading goal scorer the year before.
Rovers started confidently and were rewarded for their early endeavour after three minutes when David Bentley broke into the Arsenal box and was awkwardly hauled down by Kolo Toure.
My national side has great players like Didier Drogba, Salomon Kalou and my brother Kolo -- so I think we have as a good a chance as any team.
Minutes later, the visitors were level when City centre-back Kolo Toure made a hash of clearing a corner, allowing Henderson to smash the ball past Shay Given from 14 yards.
There were times when Campbell looked ill at ease against LuaLua's searing pace, not least when Kolo Toure had to make a last-gasp saving tackle on the DR Congo man.
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Gutierrez's initial cross was blocked by Kolo Toure but the Argentine winger collected the loose ball in the box and blasted a powerful rising shot past Hart from 10 yards.
Kolo Toure, playing at right-back because Bacary Sagna is out injured, looked a shadow of his normal self - and even Cesc Fabregas looked shockingly out of sorts in midfield.
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