Aiming to return to winning ways following their UEFA Nations League exit, France's task was made harder when Mbappe – who had squandered a great early chance – went off with a shoulder injury following an awkward collision with visiting goalkeeper Martin Campana.
But, having failed to score in the first half for a fourth successive game, France's luck changed when Martin Caceres was harshly adjudged to have handled Antoine Griezmann's effort.
Giroud made no mistake from the resulting penalty, ensuring that Mbappe's absence was not felt too much by Didier Deschamp's side.
Giroud's shot into the side netting set the tone for a strong France start, and the hosts would have been ahead in the 16th minute had Mbappe kept his chip on target.
The Paris Saint-Germain striker looked set to atone for that miss on the half-hour, but instead France were dealt a huge injury blow.
Having latched onto Tanguy Ndombele's defence-splitting pass, Mbappe was unable to avoid the onrushing Campana, landing heavily on his right shoulder and, despite attempting to carry on after receiving treatment, the youngster was replaced by Florian Thauvin.
France's pressure finally told early in the second half, though, with Giroud slotting home from 12 yards after Caceres was deemed to have intentionally used his arm to deny Griezmann's on-target effort.
They failed to build on that lead, however, and Jonathan Rodriguez nearly punished their profligacy late on, Hugo Lloris denying the substitute from close range to make sure Les Bleus ended a brilliant 2018 on a winning note
12 - Olivier Giroud has scored 12 goals with France since he turned 30 years old, no France players have scored more after their 30th birthday since World War 2. Expertise. pic.twitter.com/jIOnZbp1Jy— OptaJean (@OptaJean) November 20, 2018
What does it mean? Mbappe blow for club and country
As well as hindering France's chances of bouncing back from their defeat to Netherlands last time out, Mbappe's health could provide a problem for PSG boss Thomas Tuchel, with a crunch Champions League clash against Liverpool coming up, especially as the Ligue 1 leaders also saw Neymar substituted early due to an apparent injury in Brazil's friendly fixture against Cameroon.
Ndombele the next star off Les Bleus' conveyor belt
Ndombele has emerged as a potential star at Lyon and, having won his first cap in October, the midfielder put in an excellent display on his fourth international appearance, filling the void left by Paul Pogba's absence.
Suarez, Cavani go hiding
While Oscar Tabarez may rue a controversial penalty decision going against his side, the visitors did not offer enough going forward, with both Luis Suarez and Edinson Cavani - playing in the city where he plys his trade in club football - largely anonymous as Uruguay slumped to a fourth straight defeat.
France will start their Euro 2020 qualifying campaign in March, with the draw for the groups to be made on December 2. In the same month, Uruguay will continue their preparations for the 2019 Copa America.