City started well as David Silva almost played in Micah Richards with a through-ball before Alexandar Kolarov’s venomous volley was comfortably dealt with by Olexandr Shovkovskiy.
But they fell behind on 26 minutes when an unmarked Andriy Shevchenko met Andriy Yarmolenko’s cross, and the former Chelsea man made no mistake.
Shevchenko blazed another decent effort over the bar and could have then won a penalty but opted to stay on his feet after appearing to be tripped by Vincent Kompany.
Yaya Toure brought a decent save from Shovkovskiy as the introduction of Carlos Tevez injected some life into City, and Silva then fired wide from close range after Pablo Zabaleta’s poor effort fell to him just six yards out.
And they were made to pay when Kiev doubled their advantage 13 minutes from time, Oleh Gusev meeting a Artem Milevskiy flick-on to fire his volley into the top corner of Joe Hart’s net.
Gusev almost handed the hosts a three-goal advantage to take to Manchester for the second leg but Hart made a decent save to keep City in the tie, although they will have some serious work to do when the teams meet again.