Chelsea looked in the mood from the off and blew their opponents away in a fluid first half.
The home side went ahead inside two minutes as Willian took advantage of Hull squandering possession to advance and curl a left-footed effort beyond David Marshall and into the top corner from the edge of the box.
Olivier Giroud was twice inches away from turning home inviting low crosses, whilst the Frenchman also volleyed over after being well found by Pedro.
Chelsea looked like scoring every time they went forward, with Pedro wasting a great chance with 26 minutes on the clock by firing straight at David Marshall after some brilliant work from the impressive Willian.
Pedro made amends within a minute though as he was sent racing away over the top by Cesc Fabregas, keeping his cool to slot low past the advancing Marshall.
Just five minutes later the lead was extended further still, Willian being afforded the freedom of Stamford Bridge to advance forward and curl home low via the post from 25 yards.
16 February 2018
With just three minutes to go until the break Olivier Giroud added the icing on top of the cake, turning home at the near post for his first goal since his January move from Arsenal after being found by debutant Emerson Palmieri.
That mean Chelsea went in at the break four goals ahead and the reduced levels of intensity were evident in the second half.
- Foot off the gas -
Far from looking completely dispirited, Hull started the second half the better and were soon awarded a penalty when Harry Wilson was brought down by Fabregas in the box.
David Meyler took responsibility from the spot but his effort was well saved by Willy Caballero away to his right to cap a miserable night for Hull.
16 February 2018
Hull continued to plug away as the half wore on with Jackson Irvine forcing a regulation save from Caballero before seeing an effort deflected to safety by Ethan Ampadu.
Nouha Dicko saw a chance of his own smothered by Caballero before Marshall had to be alert to deny both Davide Zappacosta and Danny Drinkwater.
The game stuttered to a finish from then on as Chelsea secured their place in the last eight with the minimal of fuss, with attentions now turning to the Champions League clash with Barcelona in midweek.