Willian was fantastic throughout and scored the opener with a curling effort from outside the box.
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.
Hull improved slightly after the break and David Meyler had a penalty saved by Willy Caballero.
Willian almost wrapped up a first career hat-trick late on, but he hit the post from 20 yards.
Chelsea will discover their last eight opponents on Saturday at 20:00 GMT.