Leading 2-0 from the first leg, the Blues made a fast start at Stamford Bridge as Frank Lampard shot wide before Ashley Cole fired into the side-netting after some good build-up play.
Cole and Didier Drogba then combined to create an opening for Yury Zhirkov only for the defender to fire wide, and Zhirkov then attempted to turn provider for Nicolas Anelka but the Frenchman’s shot was saved by Johan Wiland.
Copenhagen almost snatched a shock opener against the run of play but Dame N’Doye’s free-kick struck the upright with Petr Cech rooted to the spot, but they were soon fighting a rearguard action once more.
Anelka raced onto Drogba’s smart pass over the top of the defence but his pull-back was fired wide by Zhirkov, and Drogba himself then wasted a glorious opportunity by diverting Jose Bosingwa’s cross wide.
John Mikel Obi headed against the crossbar and Fernando Torres had an effort deflected agonisingly wide as the Blues failed to snatch a winner late on, but the result was more than enough to put them in the final eight alongside fellow Premier League sides Manchester United and Tottenham.