Goals from Andriy Shevchenko and Oleh Gusev gave Dynamo Kiev a significant lead to take to Manchester after the Europa League last-16 first leg.
Former Chelsea and AC Milan striker Shevchenko looked lively throughout and opened the scoring when he bundled in Andriy Yarmolenko‘s 24th minute cross.
David Silva had City’s best chance but could not direct Pablo Zabaleta‘s scuffed cross towards goal.
Gusev rifled Artem Milevskiy‘s flick-on into the corner to cap a fine display.
With temperatures dipping below minus-four degrees at the Valeriy Lobanovskiy Stadium, conditions underfoot were tricky.
Unsurprisingly, it was the home side who looked far more at ease with the frozen pitch but City did produce two chances early on which suggested they might enjoy their evening in the Ukrainian capital.
First, Silva split the Dynamo defence with an incisive through-ball but Micah Richards could not get to the ball ahead of goalkeeper Olexandr Shovkovskiy.
City’s second chance after 21 minutes was the first on target by either side, but Aleksandar Kolarov’s powerful volley from 18 yards went straight into the arms of Shovkovskiy.
Once in their stride, the Ukrainian outfit’s front quartet of Shevchenko, Yarmolenko, Milevskiy and Roman Ermenko showed energy, intelligent movement and neat interplay which City found hard to suppress.
The Eastlands outfit had won four of their past five games but having left their own irrepressible energy source, 21-goal top scorer Carlos Tevez, on the bench for this clash, they lacked tempo and struggled for ideas up front.
Boss Roberto Mancini started the game with striker Edin Dzeko up front. The Bosnian had scored two against Aris Salonika in the second leg of the previous round, but service to the £27m former Wolfsburg man was limited.
Shevchenko opened the scoring when he darted to the font post unmarked and poked Yarmolenko’s cross beyond Joe Hart to record a 67th goal in European competition.
The impressive Shevchenko then blasted over the bar from 20 yards as Dynamo continued to dominate and he could have had a penalty moments later but chose not to go down when tripped by Vincent Kompany in the box.
The second half kicked off without the enigmatic Mario Balotelli on the field. The Italian had not been substituted and eventually came down the tunnel and out onto the pitch a minute later to join the game.
But with the striker clearly struggling, pointing continually to his face, he was eventually replaced by Carlos Tevez.
The introduction of Tevez sparked City to life immediately as Yaya Toure‘s low shot from 20 yards was saved well by Shovkovskiy.
The score should have been level when Zabaleta’s scuffed shot bobbled across the edge of the six-yard box but it caught Silva by surprise and the Spaniard shot wide from close range.
Dynamo, who are unbeaten since November and have not lost a European game at home since December 2009, rode out the City storm.
The home side doubled the lead when Gusev charged past Richards in the box and volleyed into the top corner after latching on to Milevskiy’s flick.
Dynamo had beaten Turkish side Besiktas 8-1 on aggregate in the last round and with City’s discipline and shape in disarray, they looked likely to add another.
Hart saved low from Gusev as the forward almost wrapped up the tie from close range.
BBC Radio 5 live’s Danny Murphy surmised: “Manchester City have been given a lesson on how to play two-legged European football.
“But at 2-0 they are still in with a decent chance of going through and can possibly turn this around at Eastlands.”
