Although Antonio Conte's men have been underwhelming of late, losing three of their previous five games in all competitions, there never looked to be any danger of a shock on Friday, with two-goal Willian and Giroud catching the eye in a ruthless display.
The match was not even two minutes old when Willian scored his sumptuous opener and, although it took a while for Chelsea to break Hull down again, the visitors caved in once the second went in.
Pedro was the man to increase their advantage with a tidy finish, before Willian doubled his tally soon after and Giroud got off the mark for the club following his January arrival from Arsenal to open up a four-goal lead by half-time.
A miserable outing got worse for Hull just after the break when Willy Caballero saved David Meyler's penalty, though Chelsea took a relaxed approach to increasing their lead, noticeably easing off after the interval.
But the comfortable scoreline allowed Conte to withdraw key men ahead of Tuesday's visit of Barcelona in the Champions League, as the Blues head into that contest in confident mood, having booked passage to the last eight of the FA Cup.
Although they were without the likes of N'Golo Kante and Eden Hazard, who were rested, Chelsea's start gave every indication that Hull were in for a long night, as Willian opened the scoring in just the second minute.
Kevin Stewart squandered possession to Giroud and he found Willian, who evaded the former Liverpool man and curled an unstoppable left-footed effort into the top-left corner from 25 yards.
Poor finishing let Chelsea down a couple of times thereafter, but they were not to be kept out for long.
Pedro raced on to Cesc Fabregas' brilliant pass over defence in the 27th minute and coolly swept past David Marshall to make it 2-0.
And a third goal soon followed – Willian finding the bottom-right corner via the post from just outside the area after good work by Giroud again.
Giroud then got in on the act himself just prior to the break, stabbing in from close range after a strong run up the left flank by debutant Emerson Palmieri.
Hull had a great chance to at least get themselves on the scoresheet early in the second half, with Fabregas tripping Harry Wilson in the area, but Caballero produced a fine save to keep Meyler's powerful spot-kick out.
Nevertheless, it could certainly be argued that Hull improved after the break, with Caballero again called into action to deny Jackson Irvine just before the hour.
Adama Diomande then troubled Caballero 22 minutes from the end, getting past Ethan Ampadu and testing the goalkeeper from a tight angle.
The wonderful Willian almost completed his hat-trick late on when hitting the post from 30 yards, but Chelsea eased to victory regardless, leaving Championship strugglers Hull to focus on preventing back-to-back relegations.
Key Opta stats:
- Chelsea have now won seven consecutive matches against Hull City in all competitions, scoring 17 goals and keeping six clean sheets.
- Chelsea's opener was scored after just 106 seconds, and there were just 288 seconds between the Blues' second and third goals.
- The Blues have progressed from 10 of their last 11 fifth round FA Cup ties, only losing against Manchester City in 2014.
- Willian has had a hand in 14 goals in his last 14 starts for Chelsea in all competitions (nine goals, five assists).
- Olivier Giroud has been directly involved in five goals in his last two appearances against Hull in all competitions (three goals, two assists). Indeed, the Frenchman has had a hand in three goals in a single match for the first time since January 2017 for Arsenal against Bournemouth.
- Willy Caballero has saved five of the last eight penalties he has faced in all competitions (excluding shootouts).
- The Tigers have failed to score in three consecutive FA Cup ties away from home against top-tier opponents for the first time since January 1909 – when they also drew their third straight blank against Chelsea.