Arteta started the game with six young players, a decision which was later vindicated as the two goals came from the youngsters.
Bukayo Saka got the visitors off to a flyer when he drove a shot into the roof of net from a tight angle just five minutes into the game.
Eddie Nketiah got the second goal for Arsenal midway through the first half before Sam Surridge pulled one back for Eddie Howe’s men late in the second half.
Arteta admitted winning against the Cherries in their own stadium with a young squad shows signs of optimism and insists he has a lot of faith in them.
"Very pleased. Always tough to come here and win, we have done it with a young team as well,” the Spanish coach told BBC Sports after the game.
"I have a lot of faith in them. I think they are developing really well. They are willing and hungry and will only get better.”
"We analyse opponents and try to generate situations that are favourable for our players.”
“I was worried with their history in the last few weeks we would concede in the last few minutes.”
“Our history with this cup is massive for the club. We need to take it step by step.”
Arsenal will now face League One side Portsmouth at Fratton Park in the next round of the FA Cup.
