The Gunners were ahead inside seven minutes when Mesut Ozil shrugged off his recent criticism to slot a low ball past Everton goalkeeper Joel Robles.
Everton, though, rallied and went into the break level following a fine counter-attack down the right by Ross Barkley, which ended up with Romelu Lukaku bundling home from close range.
Arsenal - who head to Bayern Munich next week looking to overturn a 2-0 deficit in the second leg of their Champions League last-16 clash - regrouped following the restart and went back ahead when former Everton midfielder Mikel Arteta converted a penalty, which had to be retaken following encroachment.
Giroud, who had come on for Yaya Sanogo just after the hour, made sure with a late double - the second following a sublime passing move from the resurgent hosts.
Wenger believes the performance of Giroud, who now taken his tally to 18 goal for the season, shows it was right to take him out of the front line in recent weeks, during which the 27-year-old has also refocused following personal issues off the pitch.
"It was important because he was on the end of things and shows that, when a player comes of the bench of that quality, it can make a difference," Wenger said.
"He was on the bench for what reason? He has played many games. For the rest, he has come on and showed he can score goals when he comes on. Yes (he needed a rest). Ozil was as well on the bench."
Wenger reckons Ozil answered his critics in the best way possible, the £42.5million former Real Madrid man scoring a much-needed first goal since early December.
"I hope that will encourage him," the Frenchman said. "What I liked with him is that physically he looked regenerated, having more power in his runs.
"As well what I liked, he did a lot of dirty work for a player like him - that means he tracked back in the first half, especially on the counter-attack. He came back with long runs and, when he behaves like that, of course you have a better chance to win the game."
Wenger felt Arsenal were good value for the victory, which kept them on course for a first trophy since 2005.
"We had a quality performance from the first to the last minute against a good side," he said.
"Everton started the second half well and had a good moment in the game where they had the chance with Barkley after, then we scored the second goal and then we controlled the game well."
Wenger added: "We are in the semi-final. Mathematically, I cannot deny that what you say is true (closer to a trophy), but practically it is a bit more difficult than that.
"Let us see who we have to play in the semi-final and do it again."
Wenger hopes his side can take confidence from Saturday's performance into their European tie.
"It was important for us to win, to put us in a good mind on the psychological front," he said.
"We can be inspired by our focus on the day, by our desire and go to Bayern with the same spirit.
"The statistics go against us when he go to Bayern, but let's make sure that the performance goes for us, then we have a chance."
Everton manager Roberto Martinez was left to reflect on what might have been, with England midfielder Barkley unable to convert from the edge of the box just before Arsenal went ahead from the spot.
"I felt the key moment of the game was going to the second goal and we had made it a real uncomfortable game for Arsenal," he said.
"We had a great chance and, in nine out of 10 situations like that, Ross Barkley will hit the target.
"I can see why the referee gave the penalty, although I don't agree with the decision completely, because there is contact but the ball is challenged by both of the players.
"After that, we gambled a bit and the final scoreline does not reflect what happened in the game."