Giroud headed home four minutes from the end of a game that had seemed destined to finish goalless.
Giroud headed home four minutes from the end of a game that had seemed destined to finish goalless at the Emirates Stadium.
Before Monday's 1-0 victory, Giroud had come off the bench 10 times in Premier League games this season and scored three goals, making his only club starts in the Champions League.
But Gunners boss Wenger insisted that Giroud had not had anything to prove to him despite his repeated absence from the starting line-up.
"He always makes a point when he comes on because he has scored many times when he comes in," Wenger said.
"He has qualities in our squad that are needed and that the other players have not. He's a fighter too, Olivier, and has a fantastic mentality.
"It has been frustrating for him because he didn't always play but I think we have an honest relationship.
"I have big respect for him and he knows that he was not always playing but despite that he kept a strong motivation level.
"Part of the job of a player is to be always ready, the players who are always ready will be there and the players who feel sorry for themselves get their chance and they give you one more reason to justify why you didn?t select them. The fighters are always ready."
Giroud has been kept on the bench by the fine form of Chile forward Alexis Sanchez and just as he finally gets a chance to make his mark, he may also have to compete with fit-again forward Danny Welbeck.
"We are competing and I think if I only have one striker everybody says: 'What are you doing?'" Wenger said.
"We need two or three strikers and we have Welbeck coming back so most of the time we have to make the decision depending on our opponent.
"Like today I knew they would play deep, and in the air Giroud could be the solution so I have to make the right decisions.
"We kept going and in the end when we couldn't make a difference on the ground we made it in the air with maybe the only player in our team who can do that."
Despite being left frustrated by Giroud's late intervention, which came after his physical challenge on Albion defender Gareth McAuley, Baggies boss Tony Pulis agreed with Wenger's assessment of the striker's qualities.
"Gareth has got pinned by Giroud and you can't allow him to do that because he's such a strong player," he said.
"He is excellent in the air and is untypical of what Arsene wants in lots of respects, but he has won them three points today."
The fact that Wenger is able to use an established international so sparingly is one reason why Pulis regards Arsenal as potentially strong challengers to leaders Chelsea in the second half of the season.
Albion have lost 1-0 to both teams in successive away matches and Pulis believes Chelsea will have to spend during the January transfer window to match Arsenal's depth.
"If you look at the players who were not playing and not in the team today, and then you look at Chelsea's, I think Arsenal have definitely got the stronger squad," Pulis said.
"So they have most probably got the staying power to see them through and it will be interesting to see what Chelsea do.
"I think Chelsea will spend. I don't think your man (owner Roman Abramovich) will sit back on what he's got, I think he will invest. So it will be an interesting window for the top four or five clubs."