The French forward was denied by Tim Krul before the Norwich goalkeeper tipped Christian Pulisic's ferocious strike over via the crossbar, as the visitors defended resolutely.
But in first-half stoppage time Giroud shook off his marker, Timm Klose, and sent a powerful header beyond Krul from Pulisic's cross.
After the break, Krul saved from Marcos Alonso and Willian as Chelsea were denied a second goal.
With 63 points, the Blues are in third position and four ahead of nearest rivals Leicester and Manchester United, who are in fifth.
Relegated Norwich remain bottom on 21 points.
Chelsea: 22 Jul v Liverpool (A)
Norwich: 18 Jul v Burnley (H)