Nicolas Anelka grabbed the first, a one-on-one, and sixth, a tap-in, while Florent Malouda smashed the second.
Florent Malouda slammed in a second before following up Frank Lampard's saved shot to slot in a third.
The Frenchman stooped to head home Florent Malouda's pinpoint cross to settle the game in the second half.
Florent Malouda and Salomon Kalou hit the woodwork for Chelsea, but resilient Rosenborg held out to force a draw.
Florent Malouda tapped in the fifth after Nicolas Anelka had hit the post.
Chelsea winger Florent Malouda also apologised for the events that hampered France's tournament.
Chelsea, with Nicolas Anelka at the tip of an attacking trio that also comprised Florent Malouda and Kalou, quickly responded.
The Bolton keeper made decent saves from Frank Lampard and Florent Malouda.
Walter Samuel also denied Florent Malouda and Chelsea appealed in vain for a penalty when Motta tangled with Branislav Ivanovic after a corner.
CNN: Eto'o goal sinks Chelsea as Mourinho returns in triumph
The opening period suggested it would go to plan with Roma keeper Doni kept busy by shots from Deco, Florent Malouda and Frank Lampard.
Florent Malouda went close as Chelsea dominated before Kieron Dyer was denied by Peter Cech and Diego Tristan's flick was cleared off the line.
They suffered an early blow when Juliano Belletti limped off to be replaced by Florent Malouda after struggling following an early clash with Chaplow.
After his side was refused a penalty when Florent Malouda was carelessly bundled over by Brede Hangeland, Ancelotti decided to bring on extra firepower.
Chelsea boss Avram Grant surprisingly gave Florent Malouda the nod on the left flank, while Liverpool dropped Sami Hyypia and drafted in Alvaro Arbeloa.
Frank Lampard had an early penalty saved by Thomas Sorensen before Florent Malouda fired in the opener after latching on to John Terry's fine pass.
Cole replaced the ineffectual Florent Malouda at the break and his arrival coincided with a much a greater sense of urgency from the home team.
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.
However, they could not make their numerical advantage count in the second half and French substitute Florent Malouda's consolation goal ended their hopes of qualification.
With Didier Drogba dropped to the bench, Ancelotti defended his decision to revert to a 4-3-3 formation with Nicholas Anelka and Florent Malouda supporting the Spaniard.
Chelsea only added to their goals tally eight minutes from time when Florent Malouda drove home and Nicolas Anelka tapped in a fourth in injury time.
Mourinho has made one major signing, France's player of the year Florent Malouda, who will give his team the width he says they will have this season.
Nicolas Anelka was twice narrowly off target and Frank Lampard should have done better than shoot straight at Edwin van der Sar following good work by Florent Malouda.
The Blues did improve before the break and it took a brave block by Stephen Warnock to deny Drogba when he met Florent Malouda's pull-back from the left.
Florent Malouda's snapshot was well saved by 36-year-old keeper Antonis Nikopolidis, who also kept out Carvalho's firm header after Juliano Belletti's deep free-kick was flicked on by Malouda.
Since moving from Manchester City in 2009, Sturridge has struggled to make his mark in a Chelsea side that includes forwards Anelka, Didier Drogba, Florent Malouda and Solomon Kalou.
Lampard gave Chelsea an early lead when he converted Florent Malouda's cross at the far post, but John Carew quickly put Villa level after good work by Ashley Young.
Chelsea have Florent Malouda from Lyon as their big summer signing, which seems to fit in with boss Jose Mourinho's stated intention of giving his side more width this season.
BBC: SPORT | Football | Premier League | Alan Hansen's column
As United held firm, with an ever-present menace on the counter-attack, Ancelotti made a double change with 20 minutes left, replacing Yuri Zhirkov and Drogba with Florent Malouda and Nicolas Anelka.
Moments later, Anelka's fellow Frenchman Florent Malouda broke on the right before adding a touch of swerve on his 20-yard shot which Howard did well to push away for a corner.
Drogba and his Chelsea teammate Florent Malouda thought themselves unlucky not to have been awarded penalties, while Barca's Eric Abidal argued he was unjustly sent from the field for an alleged trip.
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