City's playmaker David Silva showed his customary sublime control to take Dzeko's low cross and fire in at the near post seven minutes after the break, but QPR leveled on 69 when Bothroyd's header hit teammate Heidar Helguson in the back and deflected past wrongfooted goalkeeper Joe Hart.
It was left to a more experienced head to make Chelsea's progression to the quarter-finals secure, as Deco was given time and space in the box to collect Cole's left-wing cross, control and fire in to the bottom right-hand corner of Al Habsi's net.