In the second half, the Gunners controlled the game, scoring three goals through Laurent Koscielny and that pair of brilliant centre-forwards, Pierre-Emerick Aubameyang, racing onto Mkhitaryan's pass and rounding the goalkeeper, and Alexandre Lacazette, who dipped a superb freekick up and over the wall.
With the win Arsenal remain fourth on 56 points, while Bournemouth sit in 12th on 34 points.
"We are not looking at the table at the moment because we still have lots of games to play", he said. After we can have and get an opportunity like Saturday. Today with our supporters here, we had a good atmosphere.More news: Iran's Foreign Minister Zarif announces resignation on Instagram
Eddie Howe's men have now lost their last nine league games away from the Vitality Stadium and were second-best for much of the night as Ozil and Mkhitaryan ran riot. I am now also very proud of our players.
"We have players who can come in, and we can be a better competitive team playing a lot of matches with players with different characteristics, but who have the character to play with the level we want".
One of the reasons for Southampton delivering a flat performance could be their huge match against Fulham on Wednesday evening, one which looks like a relegation six-pointer if ever one existed.
"At home we are feeling strong, but away we need to be more consistent", Emery said.
But, with Arsenal looking unsafe going forward, the last thing the Cherries needed was to give their hosts a helping hand.