Arsenal had started the faster of the two sides with Alexandre Lacazette controversially denied a penalty before Granit Xhaka's shot skimmed off the bar.
But Chelsea grew in strength before the break as Giroud forced Petr Cech into a brilliant diving save after a fine piece of build-up play from Pedro.
However, it was the former Gunner who haunted his old club, nipping in front of Laurent Koscielny to head Emerson's cross in at the near post after 49 minutes.
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