Southampton continued to cause Arsenal problems in the early exchanges, and nearly equalised through Matt Targett who tested Leno with a fierce drive, but the German goalkeeper was equal to the effort as he parried the shot away.
Targett tested Gunners 'keeper Leno again when he burst past Stephan Lichtsteiner down the left, but two strong hands kept out his shot towards the far post.
Matteo Guendouzi is in midfield with Lucas Torreira, while Mesut Ozil and Henrikh Mkhitaryan support Pierre-Emerick Aubameyang. So I think Iwobi is giving a lot for us.
The Gunners doubled their lead in the 17th minute when Mkhitaryan added the finishing touches to another Iwobi cross.
Emery's men head to the game following a 2-0 victory over Southampton in their last Premier League encounter.
Two attacking half-time changes from the visitors did little to inspire them back into the game, and Arsenal controlled much of the second 45 minutes like a training match.
The game against Bournemouth will be held on February 27.
Bournemouth, who remain without an away win since they beat Fulham 3-0 at Craven Cottage on October 27, stay in 12th in the table.
Alexandre Lacazette has scored against 18 of the 22 Premier League teams he has faced with Arsenal.
Speaking after the match, Emery admitted that his side were starting to play to his style and even singled out Arsenal's fringe players for adapting quickly during the club's busy fixture schedule.
These are concerning times for Saints fans, and a lot of them are growing increasingly frustrated both with results, and a player who started the match against Unai Emery's men. "For us this win, and the way we played, is a positive", he added.