Former Chelsea player Patrick Bamford put Leeds ahead with its first shot of the game as Chelsea was punished on the counter-attack.
Giroud, who scored all four of Chelsea's goals in a UEFA Champions League win over Sevilla during the week, equalised just before the half-hour with an instinctive close-range finish.
Chelsea went ahead when Kurt Zouma headed in from a corner and the host finished Leeds off in stoppage-time thanks to Christian Pulisic.
