Argentina international Sergio Aguero made a 15th-minute breakthrough in Ukraine with a powerful finish from close range.
David Silva doubled City’s advantage five minutes before half-time following a precise pass from England international Raheem Sterling.
City did wobble momentarily in the second half when Nicolas Otamendi deflected Vitaliy Buyalskiy’s shot past England No1 Joe Hart.
However, Manuel Pellegrini’s side secured an emphatic first-leg win thanks to Yaya Toure’s brilliant strike in the 89th minute.
Former Manchester United striker Owen heaped praise on the Citizens following an emphatic win.
“They’ve got some of their big players back and it is great to see them get through the game unscathed,” Owen told BT Sport.
“All round brilliant night for Man City. You’d think that result puts them into the quarter-finals.”
City became the first Premier League side to secure a first leg away victory in the Champions League last 16 since 2012 after their 3-1 win.
The Citizens host Liverpool in the League Cup final at Wembley on Sunday afternoon.
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