The Blues dominated the first half and should have scored more than just the one goal, which arrived a little under halfway through thanks to Pedro's well-taken finish.
Willian doubled his side's advantage 65 minutes in with a free kick into the top corner and Hudson-Odoi, brought off the bench 12 minutes earlier, rounded off the scoring late on to all but send Chelsea through.
That came from Chelsea's opening effort of the evening, though they had been well on top until that point and turned possession into chances in the remainder of the first half.
A mixture of poor finishing and good goalkeeping from Kiev keeper Boyko kept the scoring down, however, with Pedro guilty of missing a couple of good opportunities.
The Spanish wideman fired straight at Boyko from five yards out after a couple of opposition players failed to cut out Willian's teasing cross from the right, before being denied by the visiting goalkeeper again 15 minutes later once controlling the ball and volleying on target.
Ross Barkley also squandered a good chance in between those two Pedro openings, failing to get the better of Boyko at his near post following some good movement to get in behind - a theme of the night from the Blues' perspective.
Another Pedro shot was saved late in the first half and Marcos Alonso also came close with his deflected effort, though ultimately Chelsea's profligacy - something mentioned by Maurizio Sarri in the build-up to the game - was on show once again.
Sarri saw his side make a slow start to the second period - Pedro's tame attempt eight minutes after the restart the best they could manage before the hour mark.
Dynamo, now without a win in 15 visits to England, grew in confidence and Sarri felt the need to turn to his bench with a little under a third of the game left to play.
The arrival of Ruben Loftus-Cheek immediately paid off as he forced Kiev skipper Serhiy Sydorchuk into conceding a free kick, which Willian curled over the wall and into the top-left corner from 25 yards, just like he did the last time the Ukrainian side visited this ground.
Hudson-Odoi was unleashed by Sarri for the final 12 minutes and he went on to round off the scoring late on, taking Loftus-Cheek's cushioned pass in his stride and just about getting the ball out of Boyko's reach.
Dynamo wasted their only real chance of the game a minute before Chelsea's third when Mykola Shaparenko was waiting to be played through on goal, ending the match without a single on-target attempt to their name.
Sarri's men, who now have three successive wins in all competitions, travel to the Ukraine for the return fixture in a week's time.
CHELSEA XI (4-3-3): Kepa; Zappacosta, Christensen, Luiz, Alonso; Kovacic, Jorginho (Kante 62'), Barkley (Loftus-Cheek); Pedro, Giroud, Willian (Hudson-Odoi 78')
DYNAMO KIEV XI (4-2-3-1): Boyka; Kedziora, Burda, Shabanov, Mykolenko; Sydorchuk, Shepelev; Tsygankov, Shaparenko, Buyalskiy (Sidcley 71'); Rusyn (Garmash 66')