Pedro scored the second when he slipped the ball under David Marshall after latching onto Cesc Fabregas’ excellent halfway line pass.
Willian then scored his second from 25 yards after playing a one-two with Giroud.
The France striker’s first goal since his move from Arsenal was a smart finish from close range following debutant Emerson Palmieri’s left-wing cross.
Hull improved slightly after the break and David Meyler had a penalty saved by Willy Caballero.
Chelsea will discover their last eight opponents on Saturday at 20:00 GMT.