Manuel Pellegrini's side did enough to win the game in the first half with Sergio Aguero and David Silva both scoring to underline their importance to City.
Dynamo pulled a goal back in the second half through midfielder Vitaliy Buyalskiy, but Yaya Toure's late beauty ensured that City are very much on course to reach the quarter-finals for the first time in their history.
"It was an exceptional result away from home. We couldn't have hoped for better," City captain Vincent Kompany told BT Sport.
"We could have scored many more goals. It was a Man City performance that we'd like to see more often."
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They have been eliminated by Barcelona at this stage in each of the last two seasons but this was a far kinder draw for City against opponents who were playing their first competitive match since December due to the Ukrainian winter break.
"We made lots of mistakes in the middle of the pitch and with this team of Manchester City it's not acceptable," said Dynamo coach Sergiy Rebrov, who denied the long period without a competitive game had been a factor.
He named a fringe side containing numerous untested youngsters for Sunday's 5-1 FA Cup fifth-round defeat to Chelsea but his starting XI in the Olympic Stadium was back to full strength, with Fernando the only player to keep his place.
With Joe Hart, Kompany, Toure, Silva and Aguero in the side, City are a different proposition and, after three consecutive defeats, they looked in the mood here.
They were rewarded with the opening goal a quarter of an
hour in, as a Silva corner from the left was headed down by Toure for Aguero, who controlled before lashing in his 19th goal of the season.
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Dynamo had held Premier League opponents in Chelsea to a goalless draw at home in the group stage and beat Everton 5-2 in last season's Europa League, but they struggled to handle City and Aguero fired narrowly wide midway through the first half.
With his midfield being overrun, Rebrov chose to remove Denys Garmash and send on Miguel Veloso just after the half-hour mark, but still City came and Toure forced a save from veteran goalkeeper Olexandr Shovkovskiy before the second goal arrived five minutes from half-time.
It was a superb goal too, as Aguero laid the ball off for Raheem Sterling and his low cross to the back post was turned into the net by Silva.
Nicolas Otamendi headed out a Domagoj Vida cross but Buyalskiy met the falling ball first time from 20 yards and his shot deflected into the net off the Argentine defender.
City then had Hart to thank for keeping their lead intact as he produced a strong hand low down to his right to turn away another Buyalskiy shot following a Veloso pass, but City remained a danger on the break at the other end.
The Ivorian exchanged passes with Fernandinho before curling home with his left foot from 18 yards into the far corner.