The Londoners may well need to win the competition to ensure a return to the Champions League next season as they sit sixth in the Premier League, and justified their tag as tournament favourites against the Ukrainians.
Pedro turned home an intricate backheel from Olivier Giroud to open the scoring on 17 minutes and only some wayward finishing and fine goalkeeping from Denys Boyko kept Kiev in the game before the break.
However, Willian’s sweet free-kick and substitute Hudson-Odoi’s late third gave the scoreline a fairer reflection of the 90 minutes.
A third straight victory maintains Chelsea’s momentum and a much-needed turnaround from Maurizio Sarri, who seemed on the verge of the sack just a few weeks ago.
The Italian left Eden Hazard, N’Golo Kante and Gonzalo Higuain on the bench among six changes, but Chelsea still had far too much quality for the visitors to handle early on.
Pedro took his first clear chance by prodding through Boyko’s legs, however the Spaniard should have had plenty more to show for his night’s performance.
The former Barcelona winger side-footed a gilt-edged chance straight into Boyko’s arms moments later before the Kiev ‘keeper flew to his right to deny Pedro once more after he was picked out perfectly by a raking David Luiz pass.
Mykyta Burda then deflected Marcos Alonso’s goalbound strike inches wide as Chelsea somehow had to settle for a single-goal lead at half-time.
Sarri’s side finally had the breathing space they craved 25 minutes from time when Willian curled a wonderful free-kick into the top corner.
Ruben Loftus-Cheek should have killed the tie off completely when the England international blazed over from point-blank range eight minutes from time.
Kiev had barely threatened until the final five minutes and Brazilian Sidcley missed their best chance for an away goal by miscuing a header at the near post.
But just when the visitors thought they might find a route back into the tie, Chelsea hit them on the counter-attack when Loftus-Cheek teed up Hudson-Odoi for a third that should see the 2013 winners of this competition comfortably through.
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