City were irrepressible in the opening 45 minutes, slicing through their opponents almost at will and taking a 2-0 lead with goals from Sergio Aguero and David Silva.
The hosts, however, improved dramatically after the restart and Vitaliy Buyalskiy's deflected effort reduced the arrears to fire up the home crowd and spur on the Dynamo players.
City keeper Joe Hart was forced into a superb save to deny Buyalskiy an equaliser, but Yaya Toure curled home late on to leave the tie firmly balanced in City's favour ahead of the return leg on March 15.
The English side, who reverted to a full-strength team after resting a host of players in a humiliating 5-1 FA Cup defeat by Chelsea, began with real intent, dominating possession and pressing their opponents into near submission in a classy first-half display.
The hosts, returning from their winter break, looked very much a side who had not played an official match in two and a half months.
After a minor scare for City when Hart pushed an effort from Andriy Yarmolenko on to the crossbar, the visitors took the lead after 15 minutes.
Toure headed Silva's corner into the path of Aguero, who made the most of the space he had been afforded to chest the ball down and volley sharply past keeper Olexandr Shovkovskiy for his 16th goal in his last 17 Champions League starts.
The visitors missed chances to extend the lead with Aguero flashing a shot fractionally wide and Toure forcing Shovkovskiy to palm his effort away at the near post, but it was not long before they doubled their advantage.
Silva, playing in a central playmaker role, finished off a teasing low cross from Raheem Sterling at the far post on 40 minutes after good work from Aguero.
Kiev came out in the second half with renewed vigour and reduced the deficit when Buyalskiy's rasping effort from the edge of the area took a big deflection off Nicolas Otamendi and nestled in the corner of Hart's net.
Kiev piled forward and Hart was forced into a superb low save to deny Buyalskiy an equaliser with 10 minutes remaining, but Toure put City within touching distance of the last eight when he curled in from 20 metres in the 90th minute.
(Writing by Toby Davis; editing by Ed Osmond)
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