Rosenborg were now having to defend courageously, and keeper Hirchsfeld did well to block Juliano Belletti.
Chelsea confirmed Cole's departure when they announced German midfielder Michael Ballack and right-back Juliano Belletti would also be leaving.
Late goals from Juliano Belletti and Frank Lampard condemned City to a 2-1 defeat at Stamford Bridge on Saturday.
Tevez scored a penalty after Juliano Belletti saw red for a trip on Gareth Barry before a Bellamy tap-in.
Kalou's miss was the most glaring, heading wide from six yards at the far post after an inviting cross from Juliano Belletti.
Their discontent was compounded when Bent's miskicked clearance went in off Belletti.
They were in front after seven minutes, Mateja Kezman's brilliant pass releasing Gudjohnsen, who turned Juliano Belletti and slammed home an emphatic finish.
They suffered an early blow when Juliano Belletti limped off to be replaced by Florent Malouda after struggling following an early clash with Chaplow.
Salomon Kalou began the rout, stroking in after Juliano Belletti's shot had been blocked and Belletti made it 2-0 with a stunning 30-yard shot.
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.
But his arrival could spell the end of Juliano Belletti's brief stay at Stamford Bridge after a series of mediocre performances from the Brazilian defender.
Blues striker Nicolas Anelka was played through by Belletti and beautifully controlled as he ran in between Spurs' two centre-backs only to blaze his shot over.
David James' long ball upfield was flicked on by Baros and Defoe, played onside by Belletti, raced clear and coolly slotted the ball under the on-rushing Cech.
But Tevez made it 3-1 for City with a powerful penalty into the corner after Barry had got the wrong side of Belletti, who tripped his opponent.
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.
It was through Bridge that Chelsea fashioned their opener as the left-back's cross fell to Belletti, whose shot ricocheted off two Boro defenders allowing Kalou to stroke the ball in.
He kept his head to inject greater impetus into his side with the introduction of Tom Huddlestone and the switch of Aaron Lennon to confront the nervy Juliano Belletti on the left flank.
But there was no such profligacy from Belletti when he took aim from 30 yards and arrowed a superb shot into the top corner to finally give Chelsea the second goal they deserved.
Defoe went agonisingly close on three occasions late on, but Chelsea had chances of their own with James saving well from Belletti and Alex and an attempted chip from Shaun Wright-Phillips drifted wide of the far post.
The game sprung into life 10 minutes before the interval when Ballack's header was cleared off the line by Kranjcar, while at the other end Portsmouth were unlucky not be given a penalty when Juliano Belletti appeared to handle Baros' attempted flick in the area.
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