Dynamo were aware that they faced an uphill task to reach the last eight of this competition having lost 3-0 at Stamford Bridge last week, but Chelsea effectively ended any hopes which the home side may have had within five minutes.
Chelsea continued to push for a second early goal with Loftus-Cheek seeing a low effort from inside the area tipped wide by Denys Boyko, while the goalkeeper also had to react well to keep out Giroud's header.
The home side were offering very little going forward, and Chelsea soon found their second of the evening as Giroud produced a confident first-time finish from eight yards after getting on the end of Alonso's low cross.
Hudson-Odoi had warmed into the game as the first half progressed, and the youngster helped Chelsea add a third in added-on time with Alonso turning in the winger's cross at the back post.
Dynamo showed more intent at the start of the second half with two chances going the way of Serhiy Sydorchuk, but the midfielder could only strike the post from close range after seeing his initial effort well blocked by Kepa Arrizabalaga.
That missed opportunity only resulted in Chelsea regaining their focus, and Giroud completed his hat-trick just before the hour mark when sending a header into the far corner after meeting Willian's outswinging free kick.
Alonso was not satisfied with his first-half goal, and the Spaniard was only prevented from netting a second when Boyko somehow tipped his well-struck free kick onto the post and crossbar.
Denys Harmash headed harmlessly over the crossbar as Dynamo pushed for a consolation, but Chelsea added a fifth with 12 minutes left as Hudson-Odoi capped another impressive showing for the Blues.
The teenager latched onto a precise through-ball from Giroud, and the winger held off the attention of a defender before slotting past Boyko from 12 yards out.
Giroud could have added his fourth in added-on time, but Maurizio Sarri will be more than satisfied with a performance which will only strengthen the perception that the Blues are favourites to win this competition.
DYNAMO KIEV (4-2-3-1): Boyko; Kedziora, Burda, Kadar, Mykolenko; Sydorchuk (Tche 65'), Shepelev (Andrievsky 87'); Tsygankov, Shaparenko, Sidcley (Smyrnyi 81'); Harmash
CHELSEA (4-3-3): Arrizabalaga; Zappacosta (Azpilicueta 69'), Rudiger, Christensen, Alonso; Kante (Jorginho 65'), Kovacic, Loftus-Cheek; Willian (Pedro 74'), Giroud, Hudson-Odoi