Dzeko effort enough as City beat Baggies
The Bosnian, whose double at The Hawthorns in October included a last-gasp winner, guided home a volley after 35 minutes of a Barclays Premier League clash lacking in intensity but not incident.
City, although not mathematically certain of second place, made clear Saturday's date at Wembley was their priority as they fielded a team showing eight changes.
Captain Vincent Kompany and influential players Yaya Toure, Pablo Zabaleta and Gael Clichy were rested completely while Sergio Aguero and David Silva were among those on the bench. Joe Hart, Milner and Samir Nasri were the only three men to survive from the stalemate at Swansea, meaning a whole new back four.
Aleksandar Kolarov was perhaps lucky to stay on the field when he caught Tamas on the side of the head with a high boot. The Romanian left the field for treatment, later to return bandaged up, while Kolarov escaped with a yellow card from referee Phil Dowd.
City then enjoyed a good spell as Tevez shot narrowly over from the edge of the box and Milner slammed a good chance from a dangerous Nasri cross. Jack Rodwell was then inches away from turning a Kolarov corner towards goal and Tevez rattled the crossbar with a powerful drive from the edge of the box.
The opening goal came moments later as Tevez broke away down the right and clipped back a delicate cross for Dzeko. The Bosnian, guilty of a glaring miss at Swansea, watched carefully and guided a well-weighted volley past Myhill.
The break came at a good time for West Brom and they began the second period with renewed vigour. Rosenborg smashed a free-kick against the bar after being tripped by Javi Garcia on the edge of the area and Hart then saved well from Billy Jones' follow-up header. West Brom applied pressure for a spell but were unable to break through.