Pedro and Olivier Giroud were also on the scoresheet for the team beaten in last season's final.
Chelsea started January signings Giroud and Emerson Palmieri:
Meanwhile, the Tigers fielded a familiar side with David Meyler, Michael Dawson and Evandro all involved:
The hosts were in front in the second minute when Willian curled in a beauty. Giroud had played his role in the build-up, teeing up the Brazilian with a typically smart touch.
Scoring has become common for Willian when he's been given a chance by manager Antonio Conte, per OptaJoe:
Chelsea were in the ascendancy and produced some stylish football after the goal. It should have been 2-0 when Davide Zappacosta picked out Pedro, who lofted a beautiful pass to Giroud, but the big striker could only prod over.
The Blues continued to press and Cesc Fabregas was running the show at the heart of midfield. He picked out Pedro with an astute pass, but Hull goalkeeper David Marshall just did enough to put the forward off.
Giroud went close again moments later, when a fantastic one-two between Willian and Danny Drinkwater, released the latter, whose low cross narrowly evaded the centre-forward.
Chelsea's second came on 27 minutes when another smart lay-off from Giroud found Fabregas, who played Pedro through with a terrific first-time pass. The former Barcelona attacker didn't waste the chance, slotting calmly past Marshall.
Goal's Nizaar Kinsella felt Hull paid a suitably heavy price for not putting Fabregas under pressure:
Giroud was also busy for Chelsea's third when his run left Willian with room to take his shot early and make it 3-0 in 32 minutes.
There was still time for Giroud to get the goal his performance deserved before the end of the half. The ex-Arsenal man reacted quickly to turn in Emerson's low cross with his left foot.
Hull missed the chance to gain some consolation after the break when Willy Caballero denied Meyler from the penalty spot. Fabregas had given away the penalty, but Caballero's smart stop saved his blushes.
Chelsea tried to add to their tally, but Marshall produced a superb save to turn away Drinkwater's deflected volley with less than 15 minutes to go. Willian later missed out on his hat-trick when he hit the post in the 88th minute.
The Blues didn't need a fifth goal, though, as they saw out the second half serenely to reach the last eight. On this form, last season's beaten finalists can go one better.