Captain Kompany limped off after five minutes with a muscle problem and fellow defender Nicolas Otamendi followed soon after as the hosts chalked up a 3-1 aggregate triumph that was entirely due to their first-leg victory.
There was little in terms of goalmouth action throughout the return leg at the Etihad Stadium, with City keeping a largely lifeless Kiev in check and having the game's best chance when Jesus Navas hit the post midway through the second half.
Manuel Pellegrini's team, who were knocked out in the last 16 by Barcelona in each of the last two seasons and face local rivals Manchester United in a domestic derby on Sunday, only looked like conceding at the end when keeper Joe Hart saved well from Vitaliy Buyalskiy and Olexandr Yakovenko.
"It is a very important achievement for the club," Pellegrini told BT Sport. "This is a club that is growing and will continue to develop."
City, whose Premier League title hopes were dented with a 0-0 draw at Norwich City on Saturday, suffered a further blow when Kompany was forced off with a calf problem.
Their injury woes were compounded when Otamendi was also substituted with barely 20 minutes on the clock in what was a soporific start to the encounter.
PERSISTENT ISSUE
Kompany had only returned from a calf problem in February, having been out since December, and Pellegrini said he had suffered a recurrence of what has become a persistent issue for the Belgium international.
With City under no pressure to attack having secured a comfortable first-leg advantage, and Kiev seemingly impotent up front, the first half was played like a testimonial.
It took 58 minutes for the home side to make any sort of incision into the Kiev defence as Yaya Toure exchanged quick passes with Sergio Aguero before the Argentine striker flashed his shot wide from a tight angle.
Navas then crashed an effort against the foot of the post three minutes later as the game showed signs of life while Toure fired straight at Kiev keeper Olexandr Shovkovskiy with 20 minutes to play.
Hart was forced into action in the final few moments with good blocks to deny Buyalskiy and Yakovenko on an otherwise easy night for the City keeper.
"We lost this game in Kiev," said Dynamo coach Sergei Rebrov. "But I say thank you very much to the players.
"City have big players with big experience but it is not easy now. I wish them well."
(Reporting by Toby Davis; Editing by Tony Jimenez)
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