Yevhen Khacheridi's early red card meant that the 'Blues' were always likely to dominate the ball and so it proved as Maurizio Sarri's side threatened to put the visitors to the sword.
After seeing a series of chances go begging, Giroud eventually managed to break the deadlock to put his side well on the way to their fifth win from five in Europe this term.
Pedro was picked out over the top by Cesc Fabregas, with the winger opting to hold up play and wait for support.
Giroud was quickly on the scene, peeling away to his right and sweeping a first-time left-footed finish into the far corner.