Chelsea were joined in the next round by Group E rivals Sevilla after the Spanish side won 2-1 at Krasnodar.
Chelsea started strongly and should have been ahead as early as the seventh minute, when Timo Werner flashed Hudson-Odoi's low cross over the bar with the goal at his mercy.
England international Mount was unlucky not to double the away side's lead eight minutes later when Gomis pulled off a superb save to keep out his close range effort following a Ben Chilwell pull-back.
Mendy showed the difference he has made to Chelsea with solid saves from Guirassy and Damien Da Silva towards the end of the opening period.
But Giroud pounced less than a minute into stoppage time after Gomis' save from another Werner miss bounced up, allowing the Frenchman to head Chelsea into the last 16.