Giroud lost his cool and appeared to thrust his head into QPR defender Nedum Onuoha’s forehead in the 53rd minute when Arsenal were leading 1-0 thanks to Alexis Sanchez’s first-half goal.
Tomas Rosicky doubled the lead soon after the sending-off but the hosts were left hanging on when Charlie Austin converted a penalty 11 minutes from time.
QPR, who have now lost all nine of their away league games this term, came close to an equaliser when Eduardo Vargas had a header cleared off the line while Bobby Zamora also had a penalty appeal turned down.
Arsenal survived to give Wenger his 600th victory in charge of the north London club and take them back into sixth position in the Premier League, two points behind fourth-placed Southampton.
Wenger, who looked less than pleased with Giroud when he was dismissed, said the red card changed the game.
“From the moment of the sending-off we knew we were in a battle,” the manager told the BBC. “It was a deserved red card, Olivier didn’t control himself.
“It completely changed the dynamic of the game, we were completely in control at that stage and it was quite comfortable. Olivier is a guy who, when he makes mistakes, he stands up and admits it.”
Arsenal are 15 points behind leaders Chelsea but can climb higher in the table on Sunday when they face fifth-placed West Ham United.
“We find ourselves detached from the teams above us at the moment with a bit of ground to make up so we can’t get too carried away with trying to make up that ground at the moment, we must just concentrate on what we’re doing,” Wenger said.
(Editing by Tony Jimenez)