And the French striker admitted it was a relief to get off the mark, despite already scoring in the League Cup.
"I'm so happy to score the first goal and to assist my friend Theo," Giroud said. "I hope so many goals come after this. Everyone talked to me about the [lack of a] goal, but I kept confident and concentrated on the work in training and in the games."
The result for Wenger's side puts them back on track after losing to Chelsea last weekend, despite losing Kieran Gibbs to a second-half injury.
And it means they have lost just once in the Premier League this season, after former striker Robin van Persie joined Manchester United in the summer.
Arsenal and have now leapfrogged West Ham in the table to move to fifth ahead of the international break.
"We started [the season] with many questions about us," Wenger told BBC Sport. "But of course we need to build up belief and convince people around us we have a chance.
"Apart from the Chelsea game we have been convincing and we have belief we can do something special."
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