Champions League qualification appeared to be on the rocks after third-placed Chelsea lost 3-0 to Sheffield United last time out, but after Leicester City and United dropped points too, Frank Lampard's men have consolidated their place in the driving seat.
That is not to say it was in great shape throughout at Stamford Bridge – there were times in the first half where the Blues looked like they might disappoint again, but Giroud finally punished slack defending in stoppage time.
Clear-cut chances were more of a rarity after the break, but against a Norwich side that has scored just 26 times this season, Chelsea never looked in danger of being pegged back and Giroud's header was enough.
Chelsea was dominant throughout the first half but were less than convincing in front of goal.
Giroud, starting ahead of Tammy Abraham, was guilty of spurning two excellent chances with mishit finishes, with the hosts appearing to grow frustrated as the first period progressed.
Christian Pulisic went close as well, though Tim Krul's reaction save saw him tip the American's fierce strike on to the crossbar in the 36th minute.
Giroud eventually made the breakthrough just before half-time, however, nodding in Pulisic's cross from six yards.
The second half was an even cagier affair, with little happening at either end before Cesar Azpilicueta's speculative long-range effort with his left foot flew just over.
Krul then thwarted Pulisic from close range 15 minutes from time, though Chelsea were not made to rue that error, as they saw out the triumph.