Poland striker Lewandowski gave Bayern the lead with an overhead kick after the ball fell loose in the area.
Kingsley Coman, who scored the winner in the 2020 final against Paris St-Germain, slotted home the second.
Denys Harmash scored Kyiv’s first goal of this year’s tournament but they were unable to find an equaliser.
Bayern were without Joshua Kimmich, Serge Gnabry, Jamal Musiala, Eric-Maxim Choupo-Moting and Michael Cuisance after the five players were in close contact with someone who has tested positive for Covid-19.
German newspaper Bild has reported that those players will not be paid during their quarantine period.
The 2020 winners started slowly but Lewandowski’s instinctive finish was a moment of brilliance typical of the striker.
A cross from the right popped up off a defender’s leg and the airborne striker volleyed home with his left foot.
The goal meant the 33-year-old became the first player to score in nine successive Champions League games twice, having also done it in August 2020. Ruud van Nistelrooy and Cristiano Ronaldo have both achieved the feat once.
Kyiv, who were unable to progress after picking up just one point in their first four games, hit the post at 1-0 when a Leon Goretzka back-pass was missed by Manuel Neuer as he attempted to clear.
Coman made it 2-0 just before half-time when he latched on to a Corentin Tolisso pass on the right wing and slotted into the top far corner.
Kyiv were excellent after the break, forcing Neuer into an early save, before substitute Harmash finished off a clever move to reduce the deficit.
They pushed for an equaliser, with captain Serhiy Sydorchuk seeing an effort from just outside the area saved and Viktor Tsyhankov grazing the outside of the post with a left-footed effort from distance.