Chelsea got off to the perfect start as they all but tore up any plans Nigel Adkins might have had for his side, Willian cutting inside to bend a standout finish into the far corner beyond a stranded David Marshall after just two minutes.
The visitors offered very little going forward in the first half and the Blues added their second in the 27th minute, this time as Giroud and Cesc Fabregas combined to release Pedro in behind, who made no mistake when converting one-on-one with Marshall.
Fabregas proved invaluable throughout the first period as he took control of the midfield. His efforts were matched by Giroud when creating up top and the Frenchman was central to Chelsea's third, this time feeding Willian who produced another fantastic finish from outside of the box to make it 3-0.
The contest was arguably over just before the break, as Giroud capped off a standout first-half showing by securing his first goal for the club with a deft finish following some adroit work from debutant Emerson Palmieri on the left flank.
Hull were much improved after the break and they were offered a lifeline when Fabregas brought down Harry Wilson inside the area, only for David Meyler to see the eventual spot kick kept out by Willy Caballero.
The Tigers created few chances and when Nouha Dicko eventually broke through he was soon denied by Caballero, who made a second important save of the night to keep out the visitors.
Willian might have returned to secure a deserved hat-trick at the death, but he was denied having seen his curling shot from distance beat the keeper before cannoning back off the post.
Victory for the Blues now sees them head into a crucial European encounter against Barcelona with the confidence of back-to-back wins in all competitions and a place in the sixth round of the English showpiece.
As for Adkins and his Tigers, Hull return to the Championship aiming to stave off a potential relegation scrap when they face Middlesbrough on Tuesday.
CHELSEA (3-4-3): Caballero; Rudiger, Cahill, Ampadu; Zappacosta, Drinkwater, Fabregas (Scott '62), Emerson; Willian, Giroud (Morata '70), Pedro (Hudson-Odoi '46)
HULL CITY (4-5-1): Marshall; Meyler, Dawson, MacDonald, Clark; Stewart, Wilson (Toral '55), Evandro, Irvine (Batty '88), Diomande; Dicko (Campbell '72)