Chelsea will have Michael Essien available again after suspension and he will be a huge boost for them.
Michael Essien wasted a good chance by shooting wide before Rosenborg took a shock lead after 24 minutes.
Michael Essien scored two and Salomon Kalou one for the Blues before Scott Parker grabbed a late consolation.
Ghana fielded a strong team, including Chelsea's Michael Essien, but went down to a Mohamed Aoudou goal in stoppage time.
Michael Essien of Ghana and Chelsea has the chance to retain his 2006 title after being named in the group.
Michael Essien went close with a header before the late drama unfolded.
The Premier League champions, minus Michael Essien, Frank Lampard and John Terry, head to Tyneside without a win in their last two matches.
And it reaped a reward after only three minutes when the makeshift central defensive partnership of Paulo Ferreira and Michael Essien was ruthlessly exposed.
Arsenal were instantly deflated, and Fabianski had to make fine saves from Michael Essien and Cole as Chelsea threatened to extend the victory margin.
Ashley Cole latched on to an exquisite through ball from midfielder Michael Essien but the England left-back dragged his shot wide of Sorensen's far post.
Ancelotti used half-time to replace the ineffective John Mikel Obi with first-choice holding midfielder Michael Essien and the move seemed to give Chelsea added impetus.
Michael Essien hit the bar for Chelsea before they went ahead from a disputed corner after Darren Bent's sliced clearance went in off Juliano Belletti.
Michael Essien side-footed the visitors ahead before Nicolas Anelka added to the lead when he angled in a shot and poked in from close range.
The Ivory Coast duo Didier Drogba and Salomon Kalou, Ghana's Michael Essien and Nigeria's Mikel Jon Obi are all expected to play at the tournament.
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The Blues have gone five league games without a win in a season when Terry, Frank Lampard and Michael Essien have each had spells out injured.
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Ghana had numerous scoring chances in the first half but Junior Agogo and Sulley Muntari fluffed the opportunities after key midfielder Michael Essien was taken off injured.
Ballack, who has been in impressive form himself alongside Lampard and Michael Essien in Chelsea's midfield, remains adamant the England international should have made the final six.
Didier Drogba, Michael Essien and Michael Ballack were all on the bench, though their absence was hardly noticed as Chelsea outplayed their hosts in the opening 45 minutes.
Frank Lampard and Michael Essien tried their luck - unsuccessfully - from range in the first half, but it was the other end that saw the clearer chances.
At Chelsea, goals in the last 10 minutes from Didier Drogba and Michael Essien respectively gave the Blues 1-1 draws against Birmingham and Arsenal in 2005 and 2006.
Some of the world's most identifiable soccer stars, such as Samuel Eto'o, Didier Drogba and Michael Essien hail from Africa and are feted as heroes across the continent.
Chelsea will be unable to call on Drogba, Salomon Kalou, John Obi Mikel and Michael Essien during the Africa Cup of Nations that kicks off in January in Angola.
Michael Essien's running from deep was causing United problems, but too often the midfielder was not played in when in a good position as Chelsea made the wrong decisions.
He has already made Portuguese midfielder Deco his first signing and also have the likes of Germany captain Michael Ballack and Michael Essien vying for a place alongside Lampard.
The defender was a key player of the Ghana squad - along with Chelsea's Michael Essien, and Sulley Muntari of Inter Milan - which reached the 2006 World Cup finals.
Drogba then gave Chelsea hope, if only for a matter of seconds, when he took Michael Essien's pass on his chest and drilled a low finish beyond Van der Sar.
The tactics worked for 30 minutes as Chelsea, still desperately missing Frank Lampard and Michael Essien at the heart of the midfield, dominated possession but barely threatened the home goal.
Sunderland may have been putting in the work-rate but Chelsea carried the greater threat with their crisp passing and movement, with Michael Essien putting a near post header into the side-netting.
Ancelotti took positives from improved performances from senior players like Drogba, Michael Essien and Lampard, who have all been shadows of their former selves in recent weeks after battling back from injuries.
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Yet the Ivorian played down his own chances of adding the English title to the African award, suggesting Ghanaian team-mate Michael Essien and former England international Paul Scholes should also be considered.
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